Linear \v{C}ech closure spaces

Document Type: Research Paper

Authors

1 Department of Mathematics, Christian College, Chengannur-689122, Kerala, India

2 Department of Mathematics, Catholicate College, Pathanamthitta-689645, Kerala, India

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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Main Subjects


[1] G. Birkhoff, Lattice Theory, Amer. Math. Soc. Colloq. Publ. XXV, Providence, 1967.

[2] C. Boonpok, Generalised closed sets inĖ‡Cech closed spaces, Acta. Uni. Apulensis. 22 (2010), 133-140.

[3] E. Cech, Topological spaces, Topological papers of Eduard Cech, Academia Prague, 1968.

[4] C. Chattopadhyay, Dense sets, nowhere dense sets and an ideal in generalized closure spaces, Mat. Ves. 59 (2007), 181-188.

[5] B. Joseph, A study of closure and fuzzy closure spaces, Ph.D. thesis, Cochin University, 2007.

[6] J. Khampakdee, Semi open sets in closure spaces, Ph.D. thesis, Bruno University, 2009.

[7] J. L. Pfaltz, R. E. Jamison, Closure systems and their structure, Elsevier preprint, 2001.

[8] D. N. Roth, Cech closure spaces, Ph.D. thesis, Emporia State University, 1979.

[9] T. A. Sunitha, A study on Cech closure spaces, Ph.D. thesis, Cochin University, 1994.

[10] U. M. Swamy, R. S. Rao, Algebraic topological closure operators, Southeast. Asian. Bull. Math. 26 (4) (2003), 669-678.

[11] B. Venkateswarlu, Morphisms an closure spaces and Moore spaces, IJPAM. 91 (2) (2014), 197-207.