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

The Category MAP

Buhagiar David
Miwa, Takuo
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Description
In this paper we introduce a new category MAP of continuous maps and their morphisms as an extension of both the category TOPY (of continuous maps into a fixed space Y and their morphisms) and TOP (of topological spaces and continuous maps as morphisms). Several operations in MAP are introduced such as products, fibrewise products, inverse limits, sums, fibrewise sums and direct limits. Finally we take a look at compact (perfect) maps as an object in the category MAP.