IJPAM: Volume 105, No. 2 (2015)

ON CLASSIFICATION OF SETS IN
CLUSTER TOPOLOGICAL SPACE

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


Abstract. In this paper we deals with a general concept of classification of sets in a topological space $X$ with respect to a given nonempty system $\mathcal E$ of nonempty subsets of $X$. Using system $\mathcal E$ a generalization of the classical topological notions of closed, perfect, scattered, dense in itself and nowhere dense sets is introduced and studied.

Received: September 21, 2015

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

Key Words and Phrases: $\mathcal E$-scattered set, $\mathcal E$-nowhere dense set, $\mathcal E$-first category set, Cantor-Bendixon theorem

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DOI: 10.12732/ijpam.v105i2.12 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: 2015
Volume: 105
Issue: 2
Pages: 269 - 280


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