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On Number of k-Element in Open and Clopen Topological Space With Corresponding Graph for n?4

Francis Moses Obinna* and Adeniji A. O.
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Francis Moses Obinna*: Department of Mathematics, Federal University of Technology, Minna, Nigeria
Adeniji A. O.: Department of Mathematics, University of Abuja, Abuja, Nigeria

Academic Journal of Applied Mathematical Sciences, 2019, vol. 5, issue 9, 130-135

Abstract: In this paper, we determine the number of elements defined on each topology of a topological space for open and clopen topological spaces T(n) for 1?n?4, which is called k-element. A graph of the relationship between topologies for open and clopen set for n?3 are discussed. Hence; T(n,k) is clopen for n?1 if and only if k=2n.

Keywords: K-element; Open topological space; Clopen topological space. (search for similar items in EconPapers)
Date: 2019
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Handle: RePEc:arp:ajoams:2019:p:130-135