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On $e^*$-topological Rings

Can Dalkiran, Murad Özkoç

Abstract

The main purpose of this paper is to introduce the concept of $e^*$-topological ring. This class appears as a generalized form of the class of $β$-topological rings. In addition, we have discussed the relation between the concept of $e^*$-topological ring and some other types of topological rings existing in the literature. Also, some fundamental results about $e^*$-topological rings are revealed. Furthermore, we give some counterexamples related to our results.

On $e^*$-topological Rings

Abstract

The main purpose of this paper is to introduce the concept of -topological ring. This class appears as a generalized form of the class of -topological rings. In addition, we have discussed the relation between the concept of -topological ring and some other types of topological rings existing in the literature. Also, some fundamental results about -topological rings are revealed. Furthermore, we give some counterexamples related to our results.
Paper Structure (5 sections, 16 theorems, 11 equations)

This paper contains 5 sections, 16 theorems, 11 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. $e^*$-Topological Rings
  4. MAIN RESULTS
  5. Acknowledgements

Key Result

Lemma 2.4

Ekici A function $f:(X,\tau)\to (Y,\sigma)$ is $e^*$-continuous if and only if for every $x\in X$ and for every $V\in O(Y,f(x)),$ there exists $U\in e^*O(X,x)$ such that $f[U]\subseteq V.$

Theorems & Definitions (40)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Lemma 2.4
  • Definition 3.1
  • Remark 3.2
  • Example 3.3
  • Example 3.4
  • Example 3.5
  • Theorem 3.6
  • ...and 30 more