We show that, given a subcategory C of Top closed under refinement and products, exponentiations of morphisms in Top and in C do coincide. As a consequence, we find that a map in Haus is exponentiable if and only if it is open and locally perfect.
PRESERVATION OF TOPOLOGICAL PROPERTIES UNDER EXPONENTIATION / F. CAGLIARI, S. MANTOVANI. - In: TOPOLOGY AND ITS APPLICATIONS. - ISSN 0166-8641. - 47:2(1992), pp. 149-159.
PRESERVATION OF TOPOLOGICAL PROPERTIES UNDER EXPONENTIATION
S. MANTOVANIUltimo
1992
Abstract
We show that, given a subcategory C of Top closed under refinement and products, exponentiations of morphisms in Top and in C do coincide. As a consequence, we find that a map in Haus is exponentiable if and only if it is open and locally perfect.
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