# 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
• 32 8

#### 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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