scholarly journals Two preservation results for countable products of sequential spaces

2007 ◽  
Vol 17 (1) ◽  
pp. 161-172 ◽  
Author(s):  
MATTHIAS SCHRÖDER ◽  
ALEX SIMPSON
Keyword(s):  
Topological Spaces ◽  
Product Spaces ◽  
Convergence Spaces ◽  
Countable Product ◽  
Discrete Spaces ◽  
Sequential Spaces

We prove two results for the sequential topology on countable products of sequential topological spaces. First we show that a countable product of topological quotients yields a quotient map between the product spaces. Then we show that the reflection from sequential spaces to its subcategory of monotone ω-convergence spaces preserves countable products. These results are motivated by applications to the modelling of computation on non-discrete spaces.

scholarly journals Convergence Classes of L -Filters in L , M -Fuzzy Topological Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ting Yang ◽  
Sheng-Gang Li ◽  
William Zhu ◽  
Xiao-Fei Yang ◽  
Ahmed Mostafa Khalil
Keyword(s):  
Topological Spaces ◽  
Convergence Spaces ◽  
Topological Convergence ◽  
Convergence Structure ◽  
Fuzzy Topological Spaces ◽  
The Relationship

An L , M -fuzzy topological convergence structure on a set X is a mapping which defines a degree in M for any L -filter (of crisp degree) on X to be convergent to a molecule in L X . By means of L , M -fuzzy topological neighborhood operators, we show that the category of L , M -fuzzy topological convergence spaces is isomorphic to the category of L , M -fuzzy topological spaces. Moreover, two characterizations of L -topological spaces are presented and the relationship with other convergence spaces is concretely constructed.

scholarly journals Topological Games on Product Spaces and its Fuzzification

2013 ◽  
Vol 2 ◽  
pp. 11-15
Author(s):  
Bidyanand Prasad ◽  
BP Kumar
Keyword(s):  
Topological Space ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Perfect Information ◽  
Topological Spaces ◽  
Product Spaces ◽  
Pursuit And Evasion

This paper is concerned with the introduction of an infinite positional game of pursuit and evasion over an ideal of a topological space. A topological game has been played over some new D-product and C-product spaces of two Hausdorff topological spaces. Perfect information, decisions and goals in a game may not be feasible. Hence, fuzzy set theory has been applied in this paper to obtain better results. Academic Voices, Vol. 2, No. 1, 2012, Pages 11-15 DOI: http://dx.doi.org/10.3126/av.v2i1.8278

scholarly journals Measures on countable product spaces

1969 ◽  
Vol 30 (3) ◽  
pp. 639-644 ◽  
Author(s):  
Edwin Elliott
Keyword(s):  
Product Spaces ◽  
Countable Product

Natural Covers and R-Quotient Maps

1982 ◽  
Vol 25 (4) ◽  
pp. 456-461 ◽  
Author(s):  
S. M. Karnik ◽  
S. Willard
Keyword(s):  
Comprehensive Treatment ◽  
Topological Spaces ◽  
Quotient Maps ◽  
Sequential Spaces

AbstractWe extend the comprehensive treatment of k-spaces and sequential spaces provided by Franklin's refined notion of a natural cover to kR-spaces and sR-spaces. For this purpose, an apparently unstudied class of maps of topological spaces, the class of R-quotient maps, is introduced.

The Coreflective Subcategory of Sequential Spaces

1968 ◽  
Vol 11 (4) ◽  
pp. 603-604 ◽  
Author(s):  
S. Baron
Keyword(s):  
Topological Spaces ◽  
Recent Interest ◽  
Coreflective Subcategory ◽  
Sequential Spaces ◽  
Convergent Sequences

Certain theorems of recent interest [1, 2] concerning sequential spaces may be deduced from the fact that the category of sequential spaces, is a coreflective subcategory of the category of topological spaces, J. A space is said to be sequential if it has the finest topology that permits the convergence of its convergent sequences.

Topology

2021 ◽  
pp. 126-144
Author(s):  
James Davidson
Keyword(s):  
Topological Spaces ◽  
Product Spaces ◽  
Product Topology ◽  
Weak Topologies ◽  
Tychonoff Theorem

This chapter discusses topological spaces and associated concepts, including first‐ and second‐countability, compactness, and separation properties. Weak topologies are defined. Product spaces, the product topology, and the Tychonoff theorem are treated and also ideas of embedding, compactification, and metrization.

scholarly journals Solid convergence spaces

1973 ◽  
Vol 8 (3) ◽  
pp. 443-459 ◽  
Author(s):  
M. Schroder
Keyword(s):  
Wide Class ◽  
Topological Spaces ◽  
Convergence Spaces

The category of solid convergence spaces is introduced, and shown to lie strictly between the category of all convergence spaces and that of pseudo-topological spaces. A wide class of convergence spaces, including the c-embedded spaces of Binz, is then characterized in terms of this concept. Finally, several illustrative examples are given.

A note on discrete C-embedded subspaces

2019 ◽  
Vol 69 (2) ◽  
pp. 469-473 ◽  
Author(s):  
Mehrdad Namdari ◽  
Mohammad Ali Siavoshi
Keyword(s):  
Discrete Space ◽  
Countable Subset ◽  
Topological Spaces ◽  
Discrete Spaces ◽  
Measurable Cardinals ◽  
Hewitt Realcompactification

Abstract It is shown that in some non-discrete topological spaces, discrete subspaces with certain cardinality are C-embedded. In particular, this generalizes the well-known fact that every countable subset of P-spaces are C-embedded. In the presence of the measurable cardinals, we observe that if X is a discrete space then every subspace of υ X (i.e., the Hewitt realcompactification of X) whose cardinal is nonmeasurable, is a C-embedded, discrete realcompact subspace of υ X. This generalizes the well-known fact that the discrete spaces with nonmeasurable cardinal are realcompact.

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 A better framework for first countable spaces

2003 ◽  
Vol 4 (2) ◽  
pp. 289
Author(s):  
Gerhard Preuss
Keyword(s):  
Topological Space ◽  
Uniform Space ◽  
Topological Spaces ◽  
Convergence Space ◽  
Convergence Spaces ◽  
Natural Function ◽  
Topological Construct ◽  
Countable Space ◽  
Filter Space ◽  
First Countable Space

<p>In the realm of semiuniform convergence spaces first countability is divisible and leads to a well-behaved topological construct with natural function spaces and one-point extensions such that countable products of quotients are quotients. Every semiuniform convergence space (e.g. symmetric topological space, uniform space, filter space, etc.) has an underlying first countable space. Several applications of first countability in a broader context than the usual one of topological spaces are studied.</p>

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