scholarly journals R-compact uniform spaces in the category ZUni f

Filomat ◽  
2019 ◽  
Vol 33 (5) ◽  
pp. 1463-1469
Author(s):  
Asylbek Chekeev ◽  
Tumar Kasymova
Keyword(s):  
Uniform Spaces ◽  
Normal Bases ◽  
Compact Spaces ◽  
Basic Properties ◽  
Continuous Mappings ◽  
Tychonoff Spaces

A number of basic properties of R-compact spaces in the category Tych of Tychonoff spaces and their continuous mappings are extended to the category ZUni f of uniform spaces with the special normal bases and their coz-mappings.

Perfect Maps and Epi-Reflective Hulls

1975 ◽  
Vol 27 (1) ◽  
pp. 11-24 ◽  
Author(s):  
Anthony W. Hager
Keyword(s):  
Uniform Spaces ◽  
Compact Spaces ◽  
Perfect Map ◽  
Tychonoff Spaces ◽  
Perfect Maps

The main theorems concern the relation between the - compact spaces and the -regular spaces, and their analogues in uniform spaces. In either of the categories of Tychonoff spaces or uniform spaces, let be a class of spaces, let be the epi-reflective hull of se (closed subspaces of products of members of ), let be the “onto-reflective” hull of (all subspaces of products of members of ), and let r and o be the associated functors. Let be the class of spaces which admit a perfect map into a member of . Then, is epi-reflective (and in Tych, = but in Unif, the equality fails); call the functor p.

On 𝒞ℛ-Epic Embeddings and Absolute 𝒞ℛ-Epic Spaces

2005 ◽  
Vol 57 (6) ◽  
pp. 1121-1138 ◽  
Author(s):  
Michael Barr ◽  
R. Raphael ◽  
R. G. Woods
Keyword(s):  
Locally Compact ◽  
Compact Spaces ◽  
Open Questions ◽  
Tychonoff Spaces ◽  
Locally Compact Spaces

AbstractWe study Tychonoff spaces X with the property that, for all topological embeddings X → Y, the induced map C(Y ) → C(X) is an epimorphism of rings. Such spaces are called absolute 𝒞ℛ-epic. The simplest examples of absolute 𝒞ℛ-epic spaces are σ-compact locally compact spaces and Lindelöf P-spaces. We show that absolute CR-epic first countable spaces must be locally compact.However, a “bad” class of absolute CR-epic spaces is exhibited whose pathology settles, in the negative, a number of open questions. Spaces which are not absolute CR-epic abound, and some are presented.

scholarly journals A study of uniformities on the space of uniformly continuous mappings

2020 ◽  
Vol 18 (1) ◽  
pp. 1478-1490
Author(s):  
Ankit Gupta ◽  
Abdulkareem Saleh Hamarsheh ◽  
Ratna Dev Sarma ◽  
Reny George
Keyword(s):  
Uniform Space ◽  
Uniform Spaces ◽  
Continuous Mappings ◽  
Uniformly Continuous

Abstract New families of uniformities are introduced on UC(X,Y) , the class of uniformly continuous mappings between X and Y, where (X,{\mathcal{U}}) and (Y,{\mathcal{V}}) are uniform spaces. Admissibility and splittingness are introduced and investigated for such uniformities. Net theory is developed to provide characterizations of admissibility and splittingness of these spaces. It is shown that the point-entourage uniform space is splitting while the entourage-entourage uniform space is admissible.

scholarly journals Continuity in fuzzy bitopological ordered spaces

2021 ◽  
Vol 40 (3) ◽  
pp. 681-696
Author(s):  
Runu Dhar
Keyword(s):  
Basic Properties ◽  
Properties And Characterization ◽  
Continuous Mappings ◽  
Characterization Theorems ◽  
Closed Mappings

The aim of the present paper is to introduce and study different forms of continuity in fuzzy bitopological ordered spaces. The concepts of different mappings such as pairwise fuzzy I -continuous mappings, pairwise fuzzy D -continuous mappings, pairwise fuzzy B -continuous mappings, pairwise fuzzy I -open mappings, pairwise fuzzy D -open mappings, pairwise fuzzy B -open mappings, pairwise fuzzy I -closed mappings, pairwise fuzzy D -closed mappings and pairwise fuzzy B -closed mappings have been introduced. Some of the basic properties and characterization theorems of these mappings have been investigated.

scholarly journals Paracompact-type mappings

2021 ◽  
Vol 102 (2) ◽  
pp. 62-66
Author(s):  
B.E. Kanetov ◽  
◽  
A.M. Baidzhuranova ◽  
Keyword(s):  
Uniform Space ◽  
Continuous Mapping ◽  
Uniform Spaces ◽  
Uniform Topology ◽  
Point Space ◽  
Continuous Mappings ◽  
Basic Concepts ◽  
Uniformly Continuous

Recently a new direction of uniform topology called the uniform topology of uniformly continuous mappings has begun to develop intensively. This direction is devoted, first of all, to the extension to uniformly continuous mappings of the basic concepts and statements concerning uniform spaces. In this case a uniform space is understood as the simplest uniformly continuous mapping of this uniform space into a one-point space. The investigations carried out have revealed large uniform analogs of continuous mappings and made it possible to transfer to uniformly continuous mappings many of the main statements of the uniform topology of spaces. The method of transferring results from spaces to mappings makes it possible to generalize many results. Therefore, the problem of extending some concepts and statements concerning uniform spaces to uniformly continuous mappings is urgent. In this article, we introduce and study uniformly R-paracompact, strongly uniformly R-paracompact, and uniformly R-superparacompact mappings. In particular, we solve the problem of preserving R-paracompact (respectively, strongly uniformly R-paracompact, uniformly R-superparacompact) spaces towards the preimage under uniformly R-paracompact (respectively, strongly uniformly R-paracompact, uniformly R-superparacompact) mappings.

Order-Cauchy Completions of Rings and Vector Lattices of Continuous Functions

1980 ◽  
Vol 32 (3) ◽  
pp. 657-685 ◽  
Author(s):  
F. Dashiell ◽  
A. Hager ◽  
M. Henriksen
Keyword(s):  
Continuous Functions ◽  
Topological Properties ◽  
Order Convergence ◽  
Sequential Order ◽  
Compact Spaces ◽  
Lattice Group ◽  
Vector Lattices ◽  
Topological Condition ◽  
Bounded Continuous Functions ◽  
Tychonoff Spaces

This paper studies sequential order convergence and the associated completion in vector lattices of continuous functions. Such a completion for lattices C(X) is related to certain topological properties of the space X and to ring properties of C(X). The appropriate topological condition on the space X equivalent to this type of completeness for the lattice C(X) was first identified, for compact spaces X, in [6]. This condition is that every dense cozero set S in X should be C*-embedded in X (that is, all bounded continuous functions on S extend to X). We call Tychonoff spaces X with this property quasi-F spaces (since they generalize the F-spaces of [12]).In Section 1, the notion of a completion with respect to sequential order convergence is first described in the setting of a commutative lattice group G.

scholarly journals Uniform spaces, spanier quasitopologies, and a duality for locally convex algebras

1980 ◽  
Vol 29 (1) ◽  
pp. 99-128 ◽  
Author(s):  
Eduardo J. Dubuc ◽  
Horacio Porta
Keyword(s):  
Independent Interest ◽  
Uniform Spaces ◽  
Compact Spaces ◽  
Duality Results ◽  
Locally Convex Algebras ◽  
Functional Representation ◽  
Locally Convex

AbstractGelfand-type duality results can be obtained for locally convex algebras using a quasitopological structure on the spectrum of an algebra (as opposed to the topologies traditionally considered). In this way, the duality between (commutative, with identity) C*-algebras and compact spaces can be extended to pro-C*-algebras and separated quasitopologies. The extension is provided by a functional representation of an algebra A as the algebra of all continuous numerical functions on a quasitopological space. The first half of the paper deals with uniform spaces and quasitopologies, and has independent interest.

scholarly journals Neutrosophic soft δ-topology and neutrosophic soft δ-compactness

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3441-3458
Author(s):  
Ahu Acikgoz ◽  
Ferhat Esenbel
Keyword(s):  
Basic Properties ◽  
Soft Topology ◽  
Open Set ◽  
Continuous Mappings ◽  
Regular Open

We introduce the concepts of neutrosophic soft ?-interior, neutrosophic soft quasi-coincidence, neutrosophic soft q-neighbourhood, neutrosophic soft regular open set, neutrosophic soft ?-closure, neutrosophic soft ?-closure and neutrosophic soft semi open set. It is also shown that the set of all neutrosophic soft ?-open sets is a neutrosophic soft topology, which is called the neutrosophic soft ?-topology. We obtain equivalent forms of neutrosophic soft ?-continuity. Moreover, the notions of neutrosophic soft ?-compactness and neutrosophic soft locally ?-compactness are defined and their basic properties under neutrosophic soft ?-continuous mappings are investigated.

Continuity of separately continuous mappings

2014 ◽  
Vol 64 (4) ◽  
Author(s):  
Alireza Mirmostafaee
Keyword(s):  
Continuous Function ◽  
Dense Subset ◽  
Topological Spaces ◽  
Compact Spaces ◽  
Continuous Mappings

AbstractBy means of a topological game, a class of topological spaces which contains compact spaces, q-spaces and W-spaces was defined in [BOUZIAD, A.: The Ellis theorem and continuity in groups, Topology Appl. 50 (1993), 73–80]. We will show that if Y belongs to this class, every separately continuous function f: X × Y → Z is jointly continuous on a dense subset of X × Y provided that X is σ-β-unfavorable and Z is a regular weakly developable space.

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