IJPAM: Volume 109, No. 2 (2016)

GENERALIZED NOWHERE DENSE SETS
IN CLUSTER TOPOLOGICAL SETTING

M. Matejdes
Department of Mathematics and Computer Science
Faculty of Education
Trnava University in Trnava
Priemyselná 4, 918 43 Trnava, SLOVAKIA


Abstract. The aim of the article is to generalize the notion of nowhere dense set with respect to a cluster topological space which is defined as a triplet $(X,\tau,\mathcal E)$ where $(X,\tau)$ is a topological space and $\mathcal E$ is a nonempty family of nonempty subsets of $X$. The notions of $\mathcal E$-nowhere dense and locally $\mathcal E$-scattered sets are introduced and the necessary and sufficient conditions under which the family of all $\mathcal E$-nowhere dense sets is an ideal are given.

Received: June 29, 2016

AMS Subject Classification: 54A05, 54E52, 54G12

Key Words and Phrases: cluster system, cluster topological space, ideal topological space, $\mathcal E$-scattered set, $\mathcal E$-nowhere dense set

Download paper from here.



DOI: 10.12732/ijpam.v109i2.19 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 109
Issue: 2
Pages: 459 - 467


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).