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On e-spaces and rings of real valued e-continuous functions.
- Source :
-
Applied General Topology . 2023, Vol. 24 Issue 2, p433-448. 16p. - Publication Year :
- 2023
-
Abstract
- Whenever the closure of an open set is also open, it is called e-open and if a space have a base consisting of e-open sets, it is called e-space. In this paper we first introduce and study e-spaces and e-continuous func-tions (we call a function f from a space X to a space Y an e-continuous at x 2 X if for each open set V containing f(x) there is an e-open set containing x with f(U) C V). We observe that the quasicomponent of each point in a space X is determined by e-continuous functions on X and it is characterized as the largest set containing the point on which every e-continuous function on X is constant. Next, we study the rings Ce(X) of all real valued e-continuous functions on a spaCe X. It turns out that Ce(X) coincides with the ring of real valued clopen continuous functions on X which is a C(Y) for a zero-dimensional spaCe Y whose elements are the quasicomponents of X. Using this fact we characterize the real maximal ideals of Ce(X) and also give a natural representation of its maximal ideals. Finally we have shown that Ce(X) determines the topology of X if and only if it is a zero-dimensional spaCe. [ABSTRACT FROM AUTHOR]
- Subjects :
- *COMMERCIAL space ventures
*POINT set theory
Subjects
Details
- Language :
- English
- ISSN :
- 15769402
- Volume :
- 24
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Applied General Topology
- Publication Type :
- Academic Journal
- Accession number :
- 176710852
- Full Text :
- https://doi.org/10.4995/agt.2023.17743