Linear \v{C}ech closure spaces

Subject Areas : Algebraic topology

T. M. Chacko ¹ (Department of Mathematics, Christian College, Chengannur-689122, Kerala, India)
D. Susha ² (Department of Mathematics, Catholicate College, Pathanamthitta-689645, Kerala, India)

Received: 2018-02-09 Accepted : 2018-07-07 Published : 2018-11-01

Keywords: semi-open sets, g-semi open sets, sgc-dense sets, Moore class, vector lattice, Linear v{C}ech closure spaces, relative v{C}ech closure operator, $gamma$-open sets,

Abstract :

In this paper, we introduce the concept of linear \v{C}ech closure spaces and establish the properties of open sets in linear \v{C}ech closure spaces (L\v{C}CS). Here, we observe that the concept of linearity is preserved by semi-open sets, g-semi open sets, $\gamma$-open sets, sgc-dense sets and compact sets in L\v{C}CS. We also discuss the concept of relative \v{C}ech closure operator, meet and product linear \v{C}ech closure operators. Lastly, we describe the Moore class on the L\v{C}CS and prove that it is a vector lattice with sufficient properties.

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