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The regular open-open topology for function spaces

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  • Kathryn F. Porter

Abstract

The regular open-open topology, T r o o , is introduced, its properties for spaces of continuous functions are discussed, and T r o o is compared to T o o , the open-open topology. It is then shown that T r o o on H ( X ) , the collection of all self-homeomorphisms on a topological space, ( X , T ) , is equivalent to the topology induced on H ( X ) by a specific quasi-uniformity on X , when X is a semi-regular space.

Suggested Citation

  • Kathryn F. Porter, 1996. "The regular open-open topology for function spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 19, pages 1-4, January.
    • Handle: RePEc:hin:jijmms:912901
    DOI: 10.1155/S0161171296000415
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