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Topology and its Applications, ISSN 0166-8641, 05/2019, Volume 258, pp. 79 - 99
For a compactification αX of a Tychonoff space X, the algebra of all functions f∈C(X) that are continuously extendable over αX is denoted by Cα(X). It is shown... 
Ultrafilter theorem | [formula omitted]-emdeddability | Amorphous set | Tychonoff space | Glicksberg's theorem | Axiom of choice | Independence results | Hausdorff compactification | emdeddability | Analysis | Algebra
Journal Article
Mathematical Logic Quarterly, ISSN 0942-5616, 04/2018, Volume 64, Issue 1-2, pp. 37 - 43
In the realm of Lindelöf metric spaces the following results are obtained in ZF: (i) If X=(X,d) is a Lindelöf metric space then it is both densely Lindelöf and... 
MATHEMATICS | LOGIC
Journal Article
Topology and its Applications, ISSN 0166-8641, 09/2016, Volume 210, pp. 366 - 375
We show that the negation of each one of the following statements is consistent with ZF: (i) Every sequentially compact metric space X=(X,d) is normal, i.e.,... 
Countably compact | Axiom of Choice | Complete | Totally bounded and Lebesgue metric spaces | Sequentially compact | Compact | Cofinally Cauchy sequence | MATHEMATICS | Totally bounded and Lebesgue | MATHEMATICS, APPLIED | metric spaces | COMPACTNESS | Cytokinins
Journal Article
Topology and its Applications, ISSN 0166-8641, 10/2012, Volume 159, Issue 16, pp. 3396 - 3403
We show in ZF that:(i)A countably compact metric space need not be limit point compact or totally bounded and, a limit point compact metric space need not be... 
Cantor complete | Loeb | Countably compact | Selective | Complete | Sequentially compact | Compact | Axiom of choice | Countable Tychonoff products | Totally bounded metric spaces | MATHEMATICS, APPLIED | AXIOM | MATHEMATICS | CHOICE
Journal Article
Commentationes Mathematicae Universitatis Carolinae, ISSN 0010-2628, 2018, Volume 59, Issue 3, pp. 371 - 381
Journal Article
Commentationes Mathematicae Universitatis Carolinae, ISSN 0010-2628, 2018, Volume 59, Issue 1, pp. 119 - 134
Journal Article
Quaestiones Mathematicae, ISSN 1607-3606, 05/2019, Volume 42, Issue 5, pp. 579 - 592
Given a topological space X = (X, T ), we show in the Zermelo-Fraenkel set theory ZF that: Every locally finite family of open sets of X is finite iff every... 
countably compact | E325 | Axiom of choice | pseudocompact and lightly compact topological spaces | MATHEMATICS
Journal Article
Mathematical Logic Quarterly, ISSN 0942-5616, 08/2016, Volume 62, Issue 4-5, pp. 383 - 390
We show that (i) it is consistent with ZF that there are infinite sets X on which every metric is discrete; (ii) the notion of real infinite is strictly... 
Journal Article
Mathematical logic quarterly, ISSN 0942-5616, 08/2016, Volume 62, Issue 4-5, pp. 383 - 390
Journal Article
Topology and its Applications, ISSN 0166-8641, 04/2018, Volume 238, pp. 45 - 53
Given a metric space X=(X,d) we show in ZF that: (a) The following are equivalent: (i) For every two closed and disjoint subsets A,B of X, d(A,B)>0. (ii) Every... 
Lebesgue and normal metric spaces | Axiom of Choice | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
The Journal of Symbolic Logic, ISSN 0022-4812, 9/2010, Volume 75, Issue 3, pp. 996 - 1006
Journal Article
Topology and its Applications, ISSN 0166-8641, 12/2017, Volume 232, pp. 256 - 266
Let X=(X,d), Y=(Y,ρ) be two metric spaces and f:X→Y be a function. f is called almost-bounded iff for every ε>0 there exists a δ>0 such that for every A⊆X if... 
Totally bounded | UC and Lebesgue metric spaces | Compact | Complete | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
04/2020
A cuf space (set, resp.) is a space (set, resp.) which is a countable union of finite subspaces (subsets, resp.). It is proved in $\mathbf{ZF}$ (with the... 
Mathematics - General Topology
Journal Article
01/2020
A denumerable cellular family of a topological space $\mathbf{X}$ is an infinitely countable collection of pairwise disjoint non-empty open sets of $... 
Mathematics - General Topology
Journal Article
Topology Proceedings, ISSN 0146-4124, 2017, Volume 49, pp. 121 - 133
Conference Proceeding
Topology and its Applications, ISSN 0166-8641, 2011, Volume 158, Issue 17, pp. 2279 - 2286
Within the framework of Zermelo–Fraenkel set theory ZF, we investigate the set-theoretical strength of the following statements: (1) For every family ( A i ) i... 
Axiom of choice | Compactness | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 04/2007, Volume 135, Issue 4, pp. 1205 - 1211
We show that the existence of a countable, first countable, zero-dimensional, compact Hausdorff space which is not second countable, hence not metrizable, is... 
Hausdorff spaces | Topological compactness | Topological theorems | Mathematical theorems | Second countable spaces | First countable | Axiom of choice | General topology | Topological spaces | TOPOLOGY | HORRORS | MATHEMATICS | CHOICE | MATHEMATICS, APPLIED | AXIOM
Journal Article
04/2019
A topological space is called Loeb if the collection of all its non-empty closed sets has a choice function. In this article, in the absence of the axiom of... 
Journal Article
01/2019
A metric space $\mathbf{X}$ is called densely complete if there exists a dense set $D$ in $\mathbf{X}$ such that every Cauchy sequence of points of $D $... 
Mathematics - General Topology
Journal Article
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