Function Spaces and Contractive Extensions in Approach Theory: The Role of Regularity |
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Authors: | Eva Colebunders Frédéric Mynard William Trott |
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Affiliation: | 1. Vakgroep Wiskunde, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussel, Belgi? 2. Mathematical Sciences, Georgia Southern University, POBOX 8093, Statesboro, GA, 30460, USA
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Abstract: | Two classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other, are extended to convergence-approach spaces. Characterizations are obtained for two alternative extensions of regularity to convergence-approach spaces: regularity and strong regularity. The results improve upon what is known even in the convergence case. On the way, a new notion of strictness for convergence-approach spaces is introduced. |
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