Memoirs of the Graduate School of Science and Engineering, Shimane University. Series B, Mathematics

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Memoirs of the Graduate School of Science and Engineering, Shimane University. Series B, Mathematics 34
2001-03 発行

Partial Topological Products in MAP

Buhagiar David
Miwa, Takuo
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Description
In this paper we continue with the study of the category MAP of continuous maps and their morphisms, introduced in [3]. This category is an extension of both the category TOP_Y (of continuous maps into a fixed space Y and their morphisms) and TOP (of topological spaces and continuous maps as morphisms). Partial products are used to obtain universal type theorems for T_0, Tychonoff and zero-dimensional maps. Finally we introduce zero-dimensional and strongly zero-dimensional maps and generalize some well known results in the category TOP concerning zero-dimensional and strongly zero-dimensional spaces to the category MAP.