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ON SUBMAXIMAL AND QUASI-SUBMAXIMAL SPACES

Lee, Seung-Woo;Moon, Mi-Ae;Cho, Myung-Hyun

  • Received : 2010.08.31
  • Accepted : 2010.11.18
  • Published : 2010.12.25

Abstract

The purpose of this paper is to study some properties of quasi-submaximal spaces and related examples. More precisely, we prove that if X is a quasi-submaximal and nodec space, then X is submaximal. As properties of quasi-submaximality, we show that if X is a quasi-submaximal space, then (a) for every dense $D{\subset}X$, Int(D) is dense in X, and (b) there are no disjoint dense subsets. Also, we illustrate some basic facts and examples giving the relationships among the properties mentioned in this paper.

Keywords

maximal spaces;submaximal spaces;quasi-submaximal spaces;digital planes;digital lines

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