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.

Sequence selection properties in Cp (X) with the double ideals

2021 ◽  
Vol 71 (1) ◽  
pp. 147-154
Author(s):  
Sumit Singh ◽  
Brij K. Tyagi ◽  
Manoj Bhardwaj
Keyword(s):  
Topological Space ◽  
Frequency Spectrum ◽  
Nauk Sssr ◽  
Sequence Selection ◽  
Akad Nauk Sssr ◽  
Covering Properties ◽  
Selection Principles ◽  
Normal Convergence

Abstract Recently Bukovský, Das and Šupina [Ideal quasi-normal convergence and related notions, Colloq. Math. 146 (2017), 265–281] started the study of sequence selection properties (𝓘, 𝓙-α 1) and (𝓘, 𝓙-α 4) of Cp (X) using the double ideals, where 𝓘 and 𝓙 are the proper admissible ideals of ω, which are motivated by Arkhangeľskii local αi -properties [The frequency spectrum of a topological space and the classification of spaces, Dokl. Akad. Nauk SSSR 13 (1972), 1185–1189]. In this paper, we obtain some characterizations of (𝓘, 𝓙-α 1) and (𝓘, 𝓙-α 4) properties of Cp (X) in the terms of covering properties and selection principles. Under certain conditions on ideals 𝓘 and 𝓙, we identify the minimal cardinalities of a space X for which Cp (X) does not have (𝓘, 𝓙-α 1) and (𝓘, 𝓙-α 4) properties.

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.

scholarly journals On Weak Vitali Covering Properties

1978 ◽  
Vol 21 (3) ◽  
pp. 339-345 ◽  
Author(s):  
B. S. Thomson
Keyword(s):  
Exact Solution ◽  
Orlicz Spaces ◽  
Covering Property ◽  
Intimate Connection ◽  
Differentiation Theory ◽  
Covering Properties ◽  
Necessary And Sufficient

There are now a number of Vitali covering properties which have been defined to handle problems arising in differentiation theory. Although some of these have received a unified treatment, as for example in the setting of Orlicz spaces in [1, p. 168], the underlying simplicity can be lost and the intimate connection with the original weak Vitali covering property of de Possel obscured. In this note we present an exposition of a family of covering properties and show how the original methods of de Possel in [4] can be pushed to provide an exact solution of the problem of determining necessary and sufficient covering properties for a basis which is known to differentiate a given class of integrals.

scholarly journals Selective properties of fuzzy 2-metric spaces

2020 ◽  
Vol 12 (2) ◽  
pp. 67-73
Author(s):  
Lj.D.R. Kočinac ◽  
V. Çetkin ◽  
D. Dolićanin-Đekić
Keyword(s):  
Metric Spaces ◽  
Covering Properties ◽  
Selection Principles

We introduce and study some selective covering properties in fuzzy 2-metric spaces. These properties are related to the classical covering properties of Menger, Hurewicz and Rothberger which are well known in selection principles theory.

scholarly journals Covering properties of continua and mappings

2003 ◽  
Vol 74 (88) ◽  
pp. 115-120
Author(s):  
Janusz Charatonik
Keyword(s):  
Monotone Mappings ◽  
Covering Property ◽  
Covering Properties

It is known that monotone mappings preserve the covering property for continua Similar result is proved for having the covering property hereditarily. An example is constructed which shows that the two results cannot be extended to almost monotone mappings.

scholarly journals Notes on Modifications of A wQN-Space

2014 ◽  
Vol 58 (1) ◽  
pp. 129-136
Author(s):  
Jaroslav Šupina
Keyword(s):  
Topological Space ◽  
Sequence Selection ◽  
Selection Principles

Abstract We continue to investigate the generalizations of the notion of wQN-space introduced by [L. Bukovský-J. Šupina: Modifications of sequence selection principles, Topology Appl. 160 (2013), 2356-2370] and by [J. Šupina: On Ohta-Sakai’s properties of a topological space (to appear)]. We present covering characterizations, slightly different formulations, and some new relations among them

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.

On weaker forms of the chain (F) condition and metacompactness-like covering properties in the product spaces

2013 ◽  
Vol 11 (9) ◽  
Author(s):  
Süleyman Önal ◽  
Çetin Vural
Keyword(s):  
Topological Space ◽  
Countable Family ◽  
Product Spaces ◽  
Finitely Generated ◽  
Countable Product ◽  
Covering Properties

AbstractWe introduce the concept of a family of sets generating another family. Then we prove that if X is a topological space and X has W = {W(x): x ∈ X} which is finitely generated by a countable family satisfying (F) which consists of families each Noetherian of ω-rank, then X is metaLindelöf as well as a countable product of them. We also prove that if W satisfies ω-rank (F) and, for every x ∈ X, W(x) is of the form W 0(x) ∪ W 1(x), where W 0(x) is Noetherian and W 1(x) consists of neighbourhoods of x, then X is metacompact.

scholarly journals Ordinal compactness

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1117-1145
Author(s):  
Paolo Lipparini
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Refined Theory ◽  
Covering Property ◽  
Compact Topological Space ◽  
Order Types ◽  
Regular Cardinals ◽  
Small Cardinality

We introduce a new covering property, defined in terms of order types of sequences of open sets, rather than in terms of cardinalities. The most general form depends on two ordinal parameters. Ordinal compactness turns out to be a much more varied notion than cardinal compactness. We prove many nontrivial results of the form ?every [?,?]-compact topological space is [?',?']-compact?, for ordinals ?,?, ?'and ?' while only trivial results of the above form hold, if we restrict to regular cardinals. Counterexamples are provided showing that many results are optimal. Many spaces satisfy the very same cardinal compactness properties, but have a broad range of distinct behaviors, as far as ordinal compactness is concerned. A much more refined theory is obtained for T1 spaces, in comparison with arbitrary topological spaces. The notion of ordinal compactness becomes partly trivial for spaces of small cardinality.

scholarly journals On Fuzzy L-paracompact Topological Spaces

2021 ◽  
Vol 8 ◽  
pp. 38-40
Author(s):  
Francisco Gallego Lupiáñez
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Locally Compact ◽  
Hausdorff Topological Space ◽  
Characteristic Map ◽  
Covering Properties ◽  
Fuzzy Topological Space

The aim of this paper is to study fuzzy extensions of some covering properties defined by L. Kalantan as a modification of some kinds of paracompactness-type properties due to A.V.Arhangels'skii and studied later by other authors. In fact, we obtain that: if (X,T) is a topological space and A is a subset of X, then A is Lindelöf in (X,T) if and only if its characteristic map χ_{A} is a Lindelöf subset in (X,ω(T)). If (X,τ) is a fuzzy topological space, then, (X,τ) is fuzzy Lparacompact if and only if (X,ι(τ)) is L-paracompact, i.e. fuzzy L-paracompactness is a good extension of L-paracompactness. Fuzzy L₂-paracompactness is a good extension of L₂- paracompactness. Every fuzzy Hausdorff topological space (in the Srivastava, Lal and Srivastava' or in the Wagner and McLean' sense) which is fuzzy locally compact (in the Kudri and Wagner' sense) is fuzzy L₂-paracompact

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