Memoirs of the Faculty of Education, Shimane University. Natural science

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Memoirs of the Faculty of Education, Shimane University. Natural science 5
1971-12-20 発行

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Topologies on Equicontinuous Families of Mappings
Karube, Takashi
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It is well-known that equicontinuous families of mappings are important in Analysis through Ascoli's theorem. On the other hand, the topologies on them are fundamental to consider the problem when a locally equicontinuous group of transformations of a space becomes a locally compact transformation group. The problem will be treated in T. Karube [5] to which the present paper is a preliminary. Because a set-entourage uniformity on the family of all continuous mappings of a uniform space into itself must be the uniformity of compact-convergence under natural conditions (T. Karube [4]), we will set importace on the compact-open topology.