Almost separable spaces

Document Type : Original Article

Authors

Sagarmoy Bag ¹

Ram Chandra Manna ²

Sourav Kanti Patra ³

¹ Bangabasi Evening College, 19 Rajkumar Chakraborty Sarani, Kolkata-700009, West Bengal, India

² Ramakrishna Mission Vidyamandir, Belur Math, Howrah-711202, West Bengal, India

³ Department of Pure and Applied Science, Midnapore City College, Kuturia, Bhadutala-721129, West Bengal, India

10.22034/kjm.2022.267072.2136

Abstract

In this article, we introduce the notion of almost separable space, which is a generalization of separable space. We show that like separability, almost separability is $c$-productive and the converse is true under some restrictions. We discuss about the cardinality of the set of all real valued continuous functions on an almost separable space. Finally, we establish a Baire Category Like theorem on pseudocompact space.

Keywords

Almost separable space

Pseudocompact space

Functionally Hausdorff space

Sequentially separable space

Strongly sequentially separable space

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