Abstract
It is well known that the mI-topology is a generalization of the mtopology on C(X), see [1]. Given two subsets A,B ⊆ X such that A ∪ B = X, we are going to define a topology on C(X) namely the m(A,B)-topology, finer than the m-topology and C(X) with this topology becomes a topological ring. Connectedness in this space is studied and it is shown that if A,B are closed realcompact subsets of X, then the component of the zero function in C(X) with m(A,B)-topology is the ideal CK(X). Mathematics Subject Classification: 54C40
Highlights
Throughout this paper we denote by C(X) (C∗(X)) the ring of all real valued continuous functions on a completely regular Hausdorff space X
Farshid Manshoor and Farhad Manshoor as a base for a neighborhood system at f, for each f ∈ C(X) and u ∈ U+, where U+ is the set of all positive elements of C(X)
The m-topology is first introduced in the late 40s in [2] and later the research in this area became active over the last 20 years, for example, the works in [1], [3] and [4]
Summary
Copyright c 2014 Farshid Manshoor and Farhad Manshoor. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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