Generalized topological function spaces and a classification of generalized computer topological spaces (original) (raw)

On functions between generalized topological spaces

Applied General Topology, 2013

This paper investigates generalized topological spaces and functions between such spaces from the perspective of change of generalized topology. In particular, it considers the preservation of generalized connectedness properties by various classes of functions between generalized topological spaces.

On generalized topological spaces

2009

In this paper a systematic study of the category GTS of generalized topological spaces (in the sense of H. Delfs and M. Knebusch) and their strictly continuous mappings begins. Some completeness and cocompleteness results are achieved. Generalized topological spaces help to reconstruct the important elements of the theory of locally definable and weakly definable spaces in the wide context of weakly topological structures.

On generalized topological spaces I

Annales Polonici Mathematici, 2013

Topological Spaces and Continuous Functions

1989

The paper contains a definition of topological space. The following notions are defined: point of topological space, subset of topological space, subspace of topological space, and continuous function.

On some new classes of generalized continuous maps

International Journal of Contemporary Mathematical Sciences, 2016

In this paper we introduce and study the concepts of two new classes of maps, namely (µg, λ)-continuous maps, which is included by the class of (µ, λ)-continuous maps; and the class of (µg, λg)-irresolute maps. Moreover, we introduce the concepts of µg-compactness and µg-connectedness of generalized topological spaces.

On   -Homeomorphisms In Topological Spaces

Journal of Mathematical Sciences & Computer Applications

In this paper, we first introduce a new class of closed map called   -closed map. Moreover, we introduce a new class of homeomorphism called   - Homeomorphism, which are weaker than homeomorphism. We also introduce  - Homeomorphisms and prove that the set of all   - Homeomorphisms form a group under the operation of composition of maps.2000 Math Subject Classification: 54C08, 54D05.

Function spaces

Topology and its Applications, 1997

For a completely regular space X and a normed space E let Ck (X, E) (respectively C,(X, E)) be the set of all E-valued continuous maps on X endowed with the compact-open (respectively pointwise convergence) topology. We prove that some topological properties P satisfy the following conditions: (1) if Ck(X, E) and Ck(Y,F) (respectively C&(X, E) and C,(Y,F)) are linearly homeomorphic, then X E P if and only if Y E P; (2) if there is a continuous linear surjection from Ck (X, E) onto Cp(Y, F), then Y E P provided X E P; (3) if there is a continuous linear injection from Ck (X, E) into C,(Y, F), then X has a dense subset with the property P provided Y has a dense subset with the same property. 0 1997 Elsevier Science B.V.

Topics in Generalized Topology and Fuzzy Generalized Continuities

2014

Topics in Generalized Topology and Fuzzy Generalized Continuities This work is comprised of the generalized topology, algebraic generalized topology and fuzzy generalized topology. We have defined and studied the notions of semi-local function, global function, global closure operator, global interior and-normal spaces in Ideal generalized topological spaces. Properties of these functions are investigated. Examples and counter examples are given where deemed necessary. We continued the investigations of some important results in generalized topological groups and proved basic properties of-connectedness. Along with other results, it is proved that in a-topological group, the maximal-connected components containing the identity of the group is-closed invariant subgroup.-quotients of-topological groups are also discussed.-topological vector spaces (generalization of TVS) are one of the interesting structures which is defined and investigated over here. This space is a blend of-topological structure with the algebraic concept of a vector space in such a way that vector addition and scalar multiplication are-continuous functions. A counter example is given to show that a-topological vector space is not a topological vector space. We have studied the concept of a fuzzy generalized topology which is a generalization of Chang's fuzzy topology, and investigated some properties of its structure. We have also introduced the concept of fuzzy generalized open function and fuzzy generalized closed function in terms of fuzzy generalized interior and fuzzy generalized closure operators 9 2.1-Topological Spaces .2 Ideal-Topological Spaces 16 .3-semi compatible with an ideal .4 lobal functions Ideal-Topological Spaces .5 lobal closure and Global interior 34-normal spaces 38 .7-regular spaces 3-Topological Groups 47 .

New Form Of Continuous Functions In Topological Spaces

Educational Administration: Theory and Practice, 2023

In this paper a new class of functions called semi maximal continuous, semi maximal irresolute, semi maximal semi continuous, super maximal semi continuous and super semi maximal continuous functions are introduced and investigated. A function : X → Y is said to semi maximal continuous if for every maximal open set M in Y,  −1 (M) is semi maximal open set in X. During this process, some of their properties are obtained.

A study of topological structures on equi-continuous mappings

arXiv: General Mathematics, 2019

Function space topologies are developed for EC(Y,Z), the class of equi-continuous mappings from a topological space Y to a uniform space Z. Properties such as splittingness, admissibility etc. are defined for such spaces. The net theoretic investigations are carried out to provide characterizations of splittingness and admissibility of function spaces on EC(Y,Z). The open-entourage topology and point-transitive-entourage topology are shown to be admissible and splitting respectively. Dual topologies are defined. A topology on EC(Y,Z) is found to be admissible (resp. splitting) if and only if its dual is so.