scholarly journals PRODUCTS OF HUREWICZ SPACES IN THE LAVER MODEL

2017 ◽  
Vol 23 (3) ◽  
pp. 324-333 ◽  
Author(s):  
DUŠAN REPOVŠ ◽  
LYUBOMYR ZDOMSKYY
Keyword(s):  
Covering Properties ◽  
Hurewicz Property ◽  
Metrizable Spaces ◽  
Menger Property

AbstractThis article is devoted to the interplay between forcing with fusion and combinatorial covering properties. We illustrate this interplay by proving that in the Laver model for the consistency of the Borel’s conjecture, the product of any two metrizable spaces with the Hurewicz property has the Menger property.

Covering properties defined by preopen sets

2020 ◽  
pp. 2150035 ◽  
Author(s):  
Brij K. Tyagi ◽  
Sumit Singh ◽  
Manoj Bhardwaj
Keyword(s):  
Topological Spaces ◽  
Covering Properties ◽  
Menger Property

In this paper, we study some covering properties in topological spaces defined by preopen sets. We introduce and investigate the properties of the pre-Menger property, the almost pre-Menger property and their star versions. It is shown that the pre-Menger and the semi-Menger [Covering properties defined by semi-open sets, J. Nonlinear Sci. Appl. 9 (2016) 4388–4398] are independent properties.

scholarly journals Generalized open sets and selection properties

Filomat ◽  
2019 ◽  
Vol 33 (5) ◽  
pp. 1485-1493 ◽  
Author(s):  
Ljubisa Kocinac
Keyword(s):  
Topological Space ◽  
Covering Property ◽  
Covering Properties ◽  
Selection Principles ◽  
Menger Property

We define and study new weak versions of the classical Menger covering property. For this we use ?-open and ?-open covers of a topological space. Relations of these properties with known weak versions of the Menger property are examined. In this way we complement the study of weak covering properties defined by selection principles.

ON FULL COVERING PROPERTIES

1980 ◽  
Vol 6 (1) ◽  
pp. 77 ◽  
Author(s):  
Thomson
Keyword(s):  
Covering Properties

Universal elements for families of separable metrizable spaces

1998 ◽  
Vol 91 (6) ◽  
pp. 3387-3415
Author(s):  
D. N. Georgiou ◽  
S. D. Iliadis
Keyword(s):  
Metrizable Spaces

Relative version of star-Hurewicz property

2021 ◽  
Author(s):  
M. Bhardwaj ◽  
S. Singh ◽  
B. K. Tyagi
Keyword(s):  
Relative Version ◽  
Hurewicz Property

scholarly journals Several results on compact metrizable spaces in $$\mathbf {ZF}$$

2021 ◽  
Author(s):  
Kyriakos Keremedis ◽  
Eleftherios Tachtsis ◽  
Eliza Wajch
Keyword(s):  
Continuum Hypothesis ◽  
Compact Spaces ◽  
Power Set ◽  
Compact Metrizable Space ◽  
Permutation Models ◽  
Independence Results ◽  
The Axiom Of Choice ◽  
Metrizable Spaces ◽  
Transfer Theorems ◽  
The Continuum

AbstractIn the absence of the axiom of choice, the set-theoretic status of many natural statements about metrizable compact spaces is investigated. Some of the statements are provable in $$\mathbf {ZF}$$ ZF , some are shown to be independent of $$\mathbf {ZF}$$ ZF . For independence results, distinct models of $$\mathbf {ZF}$$ ZF and permutation models of $$\mathbf {ZFA}$$ ZFA with transfer theorems of Pincus are applied. New symmetric models of $$\mathbf {ZF}$$ ZF are constructed in each of which the power set of $$\mathbb {R}$$ R is well-orderable, the Continuum Hypothesis is satisfied but a denumerable family of non-empty finite sets can fail to have a choice function, and a compact metrizable space need not be embeddable into the Tychonoff cube $$[0, 1]^{\mathbb {R}}$$ [ 0 , 1 ] R .

Combinatorics of Thin Posets: Application to Monotone Covering Properties

Order ◽  
2010 ◽  
Vol 28 (2) ◽  
pp. 173-179 ◽  
Author(s):  
Maddalena Bonanzinga ◽  
Mikhail Matveev
Keyword(s):  
Covering Properties

Optimal metrics on metrizable spaces

1971 ◽  
Vol 22 (1) ◽  
pp. 660-663
Author(s):  
Ludvik Janos
Keyword(s):  
Metrizable Spaces

COVERING PROPERTIES OF SMALL VOLUME HYPERBOLIC 3-MANIFOLDS

1998 ◽  
Vol 07 (03) ◽  
pp. 381-392 ◽  
Author(s):  
ALEXANDER MEDNYKH ◽  
ANDREI VESNIN
Keyword(s):  
Small Volume ◽  
Whitehead Link ◽  
Covering Properties

Closed hyperbolic 3-manifolds obtained by Dehn surgeries on the Whitehead link yield interesting examples of manifolds of small volume. In the present paper these manifolds are described as 2-fold coverings of the 3-sphere branched over 3-bridge links. As a corollary, maximally symmetric [Formula: see text]-manifolds of small volume are obtained.

Real Functions, Covers and Bornologies

2021 ◽  
Vol 78 (1) ◽  
pp. 199-214
Author(s):  
Lev Bukovský
Keyword(s):  
Topological Space ◽  
Pointwise Convergence ◽  
Continuous Functions ◽  
Upper Semicontinuous ◽  
Upper Semicontinuous Functions ◽  
Covering Properties ◽  
Real Functions ◽  
Topology Of Pointwise Convergence ◽  
Semicontinuous Functions

Abstract The paper tries to survey the recent results about relationships between covering properties of a topological space X and the space USC(X) of upper semicontinuous functions on X with the topology of pointwise convergence. Dealing with properties of continuous functions C(X), we need shrinkable covers. The results are extended for A-measurable and upper A-semimeasurable functions where A is a family of subsets of X. Similar results for covers respecting a bornology and spaces USC(X) or C(X) endowed by a topology defined by using the bornology are presented. Some of them seem to be new.

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