Work In Progress
August 2019
Dilip Raghavan and Juris Steprans
The almost disjointness number in products
The almost disjointness number of the product of the finite ideal is shown to be bounded below by the minimum of the splitting and almost disjointness numbers
August 2019
Jan Pachl and Juris Steprans
DTC points in the compactification of discrete groups
Partial progress is made towards characterizing those countable, discrete groups whose Cech-Stone remainder contains a single point with which the two Arens products of all other po9nts disagree.
August 2016
Matthias Neufang, Jan Pachl and Juris Steprans
CentresWithDimensionalInvariantsMeans
The topological centre of a Banach algebra action is described and examined for the special case of a group acting on a set. A construction of Foreman is modified in this context.
July 2016
Juris Steprans
Complexity of the weakly almost periodic functions
It is shown that the set of weakly approximately periodic functions on various abelian groups is a complete co-analytic set.
August 2011
J. Steprans
Under Martin's Axiom the w*-closure of fewer than continuum singular elements of L1** is contained in the set of singular elements of L1**.
June 2011
The amenability character of a Banach algebra is defined and some elementary observations about it are made. In particular, it is shown that C(X) has countable amenability character if and only if X is metrizable.
May 2011
A question of V. Pestov on amenable actions is answered using a construction of M. Foreman.
May 2011
These are slides of a four lecture series on amenability presented at the Young Set Theorists meeting in Bonn in 2011. The last lecture contains joint work with D.Raghavan extending Foreman's group construction
Reviewed Articles
MR3910435
Set-theoretical problems concerning Hausdorff measures
Marton Elekes and Juris Steprans
Proceedings of the American Mathematical Society
147(4) 1709--1717 (2017)
doi.10.1090/proc/14372
Cardinal invariants related to sigma ideals on Euclidean space are examined.
MR3451936
Convolution continuity and SIN groups
Jan Pachl and Juris Steprans
Canadian Mathematical Bulletin
60(4) 845-854 (2017)
doi:10.4153/CMB-2017-002-9
The joint and separate continuity properties of the convolution operation on LUC(G) are studied for G a SIN group.
MR3549381
When automorphisms of P(kappa)/fin are trivial off a small set
Saharon Shelah and Juris Steprans
Fund. Math. 235
167--181 (2016)
http://dx.doi.org/10.4064/fm222-2-2016
MR3451936
Proof of the {G}hahramani-{L}au conjecture
V. Losert and M. Neufang and J. Pachl and J. Steprans
Adv. Math. 290 709--738 (2016)
http://dx.doi.org/10.1016/j.aim.2015.12.004
MR3401904
Non-trivial automorphisms of {\scrP(\BbbN)/[\BbbN]<ℵ0} from variants of small dominating number
S. Shelah and J. Steprāns
Eur. J. Math. 1 534--544 (2015)
http://dx.doi.org/10.1007/s40879-015-0058-0
MR3236763
Applications of harmonic analysis to the theory of cardinal invariants
Juris Steprans
CMS Notes 46 12--13 (2014)
MR3268711
Universal functions
P. B. Larson and A. W. Miller and J. Steprans and W. A. R. Weiss
Fund. Math. 227 197--246 (2014)
http://dx.doi.org/10.4064/fm227-3-1
MR3176143
Haar null sets and the consistent reflection of non-meagreness
M. Elekes and J. Steprāns
Canad. J. Math. 66 303--322 (2014)
http://dx.doi.org/10.4153/CJM-2012-058-5
MR3150724
Splitting families and complete separability
H. Mildenberger and D. Raghavan and J. Steprans
Canad. Math. Bull. 57 119--124 (2014)
http://dx.doi.org/10.4153/CMB-2013-027-2
MR2991425
Semigroups in which all strongly summable ultrafilters are sparse
N. Hindman and J. Steprans and D. Strauss
New York J. Math. 18 835--848 (2012)
http://nyjm.albany.edu:8000/j/2012/18_835.html
MR2926314
Continuous maps on Aronszajn trees
K. Kunen and J. A. Larson and J. Steprāns
Order 29 311--316 (2012)
http://dx.doi.org/10.1007/s11083-011-9205-5
MR3295936
Sets and extensions in the twentieth century
Juris Steprans
History of the continuum in the 20th century 73 to 144 (2012)
MR2901224
Maximal functions and the additivity of various families of null sets
J. Steprāns
Trans. Amer. Math. Soc. 364 3555--3584 (2012)
http://dx.doi.org/10.1090/S0002-9947-2012-05402-X
MR2805847
Masas in the {C}alkin algebra without the continuum hypothesis
S. Shelah and J. Steprāns
J. Appl. Anal. 17 69--89 (2011)
http://dx.doi.org/10.1515/JAA.2011.004
MR2658145
The commutant of L(H) in its ultrapower may or may not be trivial
Ilijas Farah, N. Christopher Phillips, and Juris Steprans
Mathematische Annalen 347 839--857 (2010)
DOI: 10.1007/s00208-009-0448-z
MR2467209
Analytic and coanalytic families of almost disjoint functions
B. Kastermans and J. Steprans and Y. Zhang
J. Symbolic Logic 73 1158--1172 (2008)
http://projecteuclid.org/getRecord?id=euclid.jsl/1230396911
MR2462464
Chasing Silver
A. Roslanowski and J. Steprans
Canad. Math. Bull. 51 593--603 (2008)
DOI: 10.4153/CMB-2008-059-2
MR2457482
The consistency of b=κ and s=κ+
V. Fischer and J. Steprans
Fund. Math. 201 283--293 (2008)
DOI: 10.4064/fm201-3-5
MR2353856
Possible cardinalities of maximal abelian subgroups of quotients of permutation groups of the integers
S. Shelah and J. Steprans
Fund. Math. 196 197--235 (2007)
DOI: 10.4064/fm196-3-1
MR2258628
Products of sequential CLP-compact spaces are CLP-compact
J. Steprans
Ann. Pure Appl. Logic 143 155--157 (2006)
DOI: 10.1016/j.apal.2005.03.005
MR2224048
The number of translates of a closed nowhere dense set required to cover a Polish group
A. W. Miller and J. Steprans
Ann. Pure Appl. Logic 140 52--59 (2006)
DOI: 10.1016/j.apal.2005.09.010
MR2214123
Chains of Baire class 1 functions and various notions of special trees
M. Elekes and J. Steprans
Israel J. Math. 151 179--187 (2006)
DOI: 10.1007/BF02777361
MR2198711
Geometric cardinal invariants, maximal functions and a measure theoretic pigeonhole principle
J. Steprans
Bull. Symbolic Logic 11 517--525 (2005)
http://projecteuclid.org/getRecord?id=euclid.bsl/1130335207
MR2167583
Many quotient algebras of the integers modulo co-analytic ideals
J. Steprans
Contemp. Math. Logic and its applications380 271--281 (2005)
MR2128705
Comparing the uniformity invariants of null sets for different measures
S. Shelah and J. Steprans
Adv. Math. 192 403--426 (2005)
DOI: 10.1016/j.aim.2004.04.010
MR2092071
Complete Erdos space is unstable
J. J. Dijkstra and J. Van Mill and J. Steprans
Math. Proc. Cambridge Philos. Soc. 137 465--473 (2004)
DOI: 10.1017/S0305004104007996
MR2071696
Less than 2ω many translates of a compact nullset may cover the real line
M. Elekes and J. Steprans
Fund. Math. 181 89--96 (2004)
DOI: 10.4064/fm181-1-4
MR1990584
The autohomeomorphism group of the Cech-Stone compactification of the integers
J. Steprans
Trans. Amer. Math. Soc. 355 4223--4240 (electronic) (2003)
DOI: 10.1090/S0002-9947-03-03329-4
MR1896046
Martin's axiom is consistent with the existence of nowhere trivial automorphisms
S. Shelah and J. Steprans
Proc. Amer. Math. Soc. 130 2097--2106 (electronic) (2002)
DOI: 10.1090/S0002-9939-01-06280-3
MR2032852
The uniformity invariants of the ideal of null sets in separable metric spaces
J. Steprans
Topology Proc. 26 811--818 (2001/02)
MR1923169
The almost disjointness cardinal invariant in the quotient algebra of the rationals modulo the nowhere dense subsets
J. Steprans
Real Anal. Exchange 27 795--800 (2001/02)
MR1856740
Cofinitary groups, almost disjoint and dominating families
M. Hrusak and J. Steprans and Y. Zhang
J. Symbolic Logic 66 1259--1276 (2001)
DOI: 10.2307/2695105
MR1855551
Cardinal invariants related to sequential separability
M. Hrusak and J. Steprans
S\=urikaisekikenky\=usho K\=oky\=uroku 66--74 (2001)
MR1833473
The covering numbers of Mycielski ideals are all equal
S. Shelah and J. Steprans
J. Symbolic Logic 66 707--718 (2001)
DOI: 10.2307/2695039
MR1733805
Restricted compactness properties and their preservation under products
J. Steprans and A. P. Sostak
Topology Appl. 101 213--229 (2000)
DOI: 10.1016/S0166-8641(98)00126-6
MR1777780
Unions of rectifiable curves in Euclidean space and the covering number of the meagre ideal
J. Steprans
J. Symbolic Logic 64 701--726 (1999)
DOI: 10.2307/2586494
MR1473455
Decomposing Euclidean space with a small number of smooth sets
J. Steprans
Trans. Amer. Math. Soc. 351 1461--1480 (1999)
DOI: 10.1090/S0002-9947-99-02197-2
MR1610762
Orthogonal families of real sequences
A. W. Miller and J. Steprans
J. Symbolic Logic 63 29--49 (1998)
DOI: 10.2307/2586584
MR1625478
Maximal filters, continuity and choice principles
H. Herrlich and J. Steprans
Quaestiones Math. 20 697--705 (1997)
MR1450995
Gδ-sets in topological spaces and games
W. Just and M. Scheepers and J. Steprans and P. J. Szeptycki
Fund. Math. 153 41--58 (1997)
MR1433612
Hausdorff capacity and Lebesgue measure
T. S. Salisbury and J. Steprans
Real Anal. Exchange 22 265--278 (1996/97)
MR1405489
Reaping numbers of Boolean algebras
A. Dow and J. Steprans and S. Watson
Bull. London Math. Soc. 28 591--599 (1996)
DOI: 10.1112/blms/28.6.591
MR1367140
Cardinal invariants associated with Hausdorff capacities
J. Steprans
192 147--184 (1996)
MR1314977
Sums of Darboux and continuous functions
J. Steprans
Fund. Math. 146 107--120 (1995)
MR1301530
Mutually complementary families of T1 topologies, equivalence relations and partial orders
J. Steprans and S. Watson
Proc. Amer. Math. Soc. 123 2237--2249 (1995)
DOI: 10.2307/2160963
MR1303686
A topological Banach fixed point theorem for compact Hausdorff spaces
J. Steprans and S. Watson and W. Just
Canad. Math. Bull. 37 552--555 (1994)
MR1297403
Decomposing Baire class 1 functions into continuous functions
S. Shelah and J. Steprans
Fund. Math. 145 171--180 (1994)
MR1271551
Somewhere trivial autohomeomorphisms
S. Shelah and J. Steprans
J. London Math. Soc. (2) 49 569--580 (1994)
MR1271434
Erratum: ``Maximal chains in ωω and ultrapowers of the integers'' [Arch. Math. Logic {\bf 32} (1993), no.\ 5, 305--319; {MR}1223393 (94g:03094)]
S. Shelah and J. Steprans
Arch. Math. Logic 33 167--168 (1994)
DOI: 10.1007/BF01352936
MR1261556
The σ-linkedness of the measure algebra
A. Dow and J. Steprans
Canad. Math. Bull. 37 42--45 (1994)
MR1259349
Homogeneous almost disjoint families
S. Shelah and J. Steprans
Algebra Universalis 31 196--203 (1994)
DOI: 10.1007/BF01236517
MR1253008
Dominating functions and graphs
R. Diestel and S. Shelah and J. Steprans
J. London Math. Soc. (2) 49 16--24 (1994)
MR1252708
The evolution of integration
A. Shenitzer and J. Steprans
Amer. Math. Monthly 101 66--72 (1994)
DOI: 10.2307/2325128
MR1253921
A very discontinuous Borel function
J. Steprans
J. Symbolic Logic 58 1268--1283 (1993)
DOI: 10.2307/2275142
MR1239060
Martin's axiom and the transitivity of Pc-points
J. Steprans
Israel J. Math. 83 257--274 (1993)
DOI: 10.1007/BF02784054
MR1234290
Combinatorial consequences of adding Cohen reals
J. Steprans
6 583--617 (1993)
MR1229497
Continuous colourings of closed graphs
A. Krawczyk and J. Steprans
Topology Appl. 51 13--26 (1993)
DOI: 10.1016/0166-8641(93)90011-2
MR1223393
Maximal chains in ωω and ultrapowers of the integers
S. Shelah and J. Steprans
Arch. Math. Logic 32 305--319 (1993)
DOI: 10.1007/BF01409965
MR1217174
Combinatorial properties of the ideal P2
J. Cichon and A. Roslanowski and J. Steprans and B. Weglorz
J. Symbolic Logic 58 42--54 (1993)
DOI: 10.2307/2275322
MR1186465
Countable Frechet α1-spaces may be first countable
A. Dow and J. Steprans
Arch. Math. Logic 32 33--50 (1992)
DOI: 10.1007/BF01270393
MR1168663
Topological invariants in the Cohen model
J. Steprans
Topology Appl. 45 85--101 (1992)
DOI: 10.1016/0166-8641(92)90050-A
MR1206463
Almost disjoint families of paths in lattice grids
J. Steprans
Topology Proc. 16 185--200 (1991)
MR1078638
Steprans' problems
J. Steprans
13--20 (1990)
MR1002627
Nontrivial homeomorphisms of βN\N without the continuum hypothesis
S. Shelah and J. Steprans
Fund. Math. 132 135--141 (1989)
MR985683
A model in which countable Frechet α1-spaces are first countable
A. Dow and J. Steprans
Math. Proc. Cambridge Philos. Soc. 105 473--480 (1989)
MR962545
Destroying precaliber ℵ1: an application of a &Delta-system lemma for closed sets
J. Steprans and S. Watson
Fund. Math. 129 223--229 (1988)
MR958051
A Banach space on which there are few operators
S. Shelah and J. Steprans
Proc. Amer. Math. Soc. 104 101--105 (1988)
DOI: 10.2307/2047469
MR935111
PFA implies all automorphisms are trivial
S. Shelah and J. Steprans
Proc. Amer. Math. Soc. 104 1220--1225 (1988)
DOI: 10.2307/2047617
MR932979
Some results on CDH spaces. I
J. Steprans and H. X. Zhou
Topology Appl. 28 147--154 (1988)
DOI: 10.1016/0166-8641(88)90006-5
MR932978
Cellularity of first countable spaces
J. Steprans and S. Watson
Topology Appl. 28 141--145 (1988)
DOI: 10.1016/0166-8641(88)90005-3
MR887767
Homeomorphisms of manifolds with prescribed behaviour on large dense sets
J. Steprans and W. S. Watson
Bull. London Math. Soc. 19 305--310 (1987)
DOI: 10.1112/blms/19.4.305
MR887554
Extraspecial p-groups
S. Shelah and J. Steprans
Ann. Pure Appl. Logic 34 87--97 (1987)
DOI: 10.1016/0168-0072(87)90041-8
MR801424
Strong Q-sequences and variations on Martin's axiom
J. Steprans
Canad. J. Math. 37 730--746 (1985)
MR770551
A characterization of free abelian groups
J. Steprans
Proc. Amer. Math. Soc. 93 347--349 (1985)
DOI: 10.2307/2044776
MR769852
The number of directed sets
K. J. Devlin and J. Steprans and W. S. Watson
Rend. Circ. Mat. Palermo (2) 31--41 (1984)
MR743378
The number of submodules
J. Steprans
Proc. London Math. Soc. (3) 49 183--192 (1984)
DOI: 10.1112/plms/s3-49.1.183
MR1540295
Problems and Solutions: Solutions of Advanced Problems: 6380
J. Steprans
Amer. Math. Monthly 90 649 (1983)
http://links.jstor.org/sici?sici=0002-9890(198311)90:9<649:6>2.0.CO;2-K&origin=MSN
MR1539901
Problems and Solutions: Advanced Problems: 6380-6382
J. Steprans and W. W. Meyer and H. Lam
Amer. Math. Monthly 89 214 (1982)
DOI: 10.2307/2320210
MR633292
Cardinal arithmetic and ℵ1-Borel sets
J. Steprans
Proc. Amer. Math. Soc. 84 121--126 (1982)
DOI: 10.2307/2043823
MR612014
Trees and continuous mappings into the real line
J. Steprans
Topology Appl. 12 181--185 (1981)
DOI: 10.1016/0166-8641(81)90019-5