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Research Articles

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


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

D. Raghavan and J. Steprans

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

J. Steprans

A question of V. Pestov on amenable actions is answered using a construction of M. Foreman.

May 2011

J. Steprans

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


Set-theoretical problems concerning Hausdorff measures  
Marton Elekes and Juris Steprans
Proceedings of the American Mathematical Society 
147(4) 1709--1717   (2017)

Cardinal invariants related to sigma ideals on Euclidean space are examined.


Convolution continuity and SIN groups 
Jan Pachl and Juris Steprans
Canadian Mathematical Bulletin 
60(4) 845-854   (2017)

The joint and separate continuity properties of the convolution operation on LUC(G) are studied for G a SIN group.


When automorphisms of P(kappa)/fin are trivial off a small set 
Saharon Shelah and Juris Steprans
Fund. Math.   235
 167--181  (2016)


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)


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)


Applications of harmonic analysis to the theory of cardinal invariants
Juris Steprans
CMS Notes  46  12--13  (2014)


Universal functions
P. B. Larson and A. W. Miller and J. Steprans and W. A. R. Weiss
Fund. Math.  227  197--246  (2014)


Haar null sets and the consistent reflection of non-meagreness
M. Elekes and J. Steprāns
Canad. J. Math.  66  303--322  (2014)


Splitting families and complete separability
H. Mildenberger and D. Raghavan and J. Steprans
Canad. Math. Bull.  57  119--124  (2014)


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)


Continuous maps on Aronszajn trees
K. Kunen and J. A. Larson and J. Steprāns
Order  29  311--316  (2012)


Sets and extensions in the twentieth century
Juris Steprans
History of the continuum in the 20th century  73 to 144  (2012)


Maximal functions and the additivity of various families of null sets
J. Steprāns
Trans. Amer. Math. Soc.  364  3555--3584  (2012)


Masas in the {C}alkin algebra without the continuum hypothesis
S. Shelah and J. Steprāns
J. Appl. Anal.  17  69--89  (2011)


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


Analytic and coanalytic families of almost disjoint functions 
B. Kastermans and J. Steprans and Y. Zhang
J. Symbolic Logic  73  1158--1172  (2008)


Chasing Silver
A. Roslanowski and J. Steprans
Canad. Math. Bull.  51  593--603  (2008)
DOI: 10.4153/CMB-2008-059-2


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


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


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


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


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


Geometric cardinal invariants, maximal functions and a measure theoretic pigeonhole principle
J. Steprans
Bull. Symbolic Logic  11  517--525  (2005)


Many quotient algebras of the integers modulo co-analytic ideals
J. Steprans
Contemp. Math. Logic and its applications380  271--281  (2005)


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


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


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


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


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


The uniformity invariants of the ideal of null sets in separable metric spaces
J. Steprans
Topology Proc.  26  811--818  (2001/02)


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)


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


Cardinal invariants related to sequential separability
M. Hrusak and J. Steprans
S\=urikaisekikenky\=usho K\=oky\=uroku    66--74  (2001)


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


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


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


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


Orthogonal families of real sequences
A. W. Miller and J. Steprans
J. Symbolic Logic  63  29--49  (1998)
DOI: 10.2307/2586584


Maximal filters, continuity and choice principles
H. Herrlich and J. Steprans
Quaestiones Math.  20  697--705  (1997)


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)


Hausdorff capacity and Lebesgue measure
T. S. Salisbury and J. Steprans
Real Anal. Exchange  22  265--278  (1996/97)


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


Cardinal invariants associated with Hausdorff capacities
J. Steprans
192  147--184  (1996)


Sums of Darboux and continuous functions
J. Steprans
Fund. Math.  146  107--120  (1995)


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


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)


Decomposing Baire class 1 functions into continuous functions
S. Shelah and J. Steprans
Fund. Math.  145  171--180  (1994)


Somewhere trivial autohomeomorphisms
S. Shelah and J. Steprans
J. London Math. Soc. (2)  49  569--580  (1994)


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


The σ-linkedness of the measure algebra
A. Dow and J. Steprans
Canad. Math. Bull.  37  42--45  (1994)


Homogeneous almost disjoint families
S. Shelah and J. Steprans
Algebra Universalis  31  196--203  (1994)
DOI: 10.1007/BF01236517


Dominating functions and graphs
R. Diestel and S. Shelah and J. Steprans
J. London Math. Soc. (2)  49  16--24  (1994)


The evolution of integration
A. Shenitzer and J. Steprans
Amer. Math. Monthly  101  66--72  (1994)
DOI: 10.2307/2325128


A very discontinuous Borel function
J. Steprans
J. Symbolic Logic  58  1268--1283  (1993)
DOI: 10.2307/2275142


Martin's axiom and the transitivity of Pc-points
J. Steprans
Israel J. Math.  83  257--274  (1993)
DOI: 10.1007/BF02784054


Combinatorial consequences of adding Cohen reals
J. Steprans
6  583--617  (1993)


Continuous colourings of closed graphs
A. Krawczyk and J. Steprans
Topology Appl.  51  13--26  (1993)
DOI: 10.1016/0166-8641(93)90011-2


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


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


Countable Frechet α1-spaces may be first countable
A. Dow and J. Steprans
Arch. Math. Logic  32  33--50  (1992)
DOI: 10.1007/BF01270393


Topological invariants in the Cohen model
J. Steprans
Topology Appl.  45  85--101  (1992)
DOI: 10.1016/0166-8641(92)90050-A


Almost disjoint families of paths in lattice grids
J. Steprans
Topology Proc.  16  185--200  (1991)


Steprans' problems
J. Steprans
  13--20  (1990)


Nontrivial homeomorphisms of βN\N without the continuum hypothesis
S. Shelah and J. Steprans
Fund. Math.  132  135--141  (1989)


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)


Destroying precaliber ℵ1: an application of a &Delta-system lemma for closed sets
J. Steprans and S. Watson
Fund. Math.  129  223--229  (1988)


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


PFA implies all automorphisms are trivial
S. Shelah and J. Steprans
Proc. Amer. Math. Soc.  104  1220--1225  (1988)
DOI: 10.2307/2047617


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


Cellularity of first countable spaces
J. Steprans and S. Watson
Topology Appl.  28  141--145  (1988)
DOI: 10.1016/0166-8641(88)90005-3


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


Extraspecial p-groups
S. Shelah and J. Steprans
Ann. Pure Appl. Logic  34  87--97  (1987)
DOI: 10.1016/0168-0072(87)90041-8


Strong Q-sequences and variations on Martin's axiom
J. Steprans
Canad. J. Math.  37  730--746  (1985)


A characterization of free abelian groups
J. Steprans
Proc. Amer. Math. Soc.  93  347--349  (1985)
DOI: 10.2307/2044776


The number of directed sets
K. J. Devlin and J. Steprans and W. S. Watson
Rend. Circ. Mat. Palermo (2)    31--41  (1984)


The number of submodules
J. Steprans
Proc. London Math. Soc. (3)  49  183--192  (1984)
DOI: 10.1112/plms/s3-49.1.183


Problems and Solutions: Solutions of Advanced Problems: 6380
J. Steprans
Amer. Math. Monthly  90  649  (1983)<649:6>2.0.CO;2-K&origin=MSN


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


Cardinal arithmetic and ℵ1-Borel sets
J. Steprans
Proc. Amer. Math. Soc.  84  121--126  (1982)
DOI: 10.2307/2043823


Trees and continuous mappings into the real line
J. Steprans
Topology Appl.  12  181--185  (1981)
DOI: 10.1016/0166-8641(81)90019-5