Connectedness in Syntopogenous Spaces
نویسندگان
چکیده
Introduction. In his monograph [l], Császár introduced the notion of a syntopogenous space, which generalized the notions of a topological space, a proximity space, and a uniform space. Although Császár was able to obtain many of the usual theorems of general topology in this more general setting, the basic topological notion of connectedness was not introduced at all. Mrówka and Pervin [2] have discussed the concepts of 11-connectedness and S-connectedness for uniform and proximity spaces, respectively. In this paper we shall give a definition for connectedness in syntopogenous spaces and show that it agrees with the corresponding properties in topological, proximity, and uniform spaces. Furthermore, we shall obtain some of the theorems concerning connected sets from general topology in this more general setting. Throughout, we shall use the notation due to Császár and assume a familiarity with his monograph [l].
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