島根大学教育学部紀要. 自然科学

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島根大学教育学部紀要. 自然科学 5
1971-12-20 発行

同程度連続な写像族上の位相

Topologies on Equicontinuous Families of Mappings
苅部 孝
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内容記述(抄録等)
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.