Note on $p_1$-Lindelof spaces which are not contra second countable spaces in bitopology

Author:

Acharjee Santanu1,Papadopoulos Kyriakos2,Tripathy Binod Chandra3

Affiliation:

1. Economics and Computational Rationality Group

2. Kuwait University

3. Tripura University

Abstract

In this article we show that a contra second countable bitopological space is a $p_1$-Lindelof space, but the converse is not true in general. We provide suitable example with the help of concepts of nest and interlocking from LOTS. The relation between pairwise regular spaces and $p_1$-normal spaces is studied. At the end, we propose some open questions which may enrich various concepts related to Lindelofness in a bitopological space and other areas of mathematical ideas.

Publisher

Sociedade Paranaense de Matematica

Subject

General Mathematics

Reference33 articles.

1. 1. S. Acharjee and B.C. Tripathy, Strategies in mixed budget: a bitopological approach,(accepted).

2. 2. T. Birsan,Compacite dens les espaces bitopologiques, An.St.Univ. Iasi.s.I.a mathematica, 15 (1969), 317-328 .

3. Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof

4. 4. H. Bouseliana and A. Kilicman, Mappings on pairwise para-Lindelof bitopological spaces, Jour. Egyptian Math. Soc., 23 (2015), 377-381.

5. On bitopological compactness

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