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Function Spaces and Contractive Extensions in Approach Theory: The Role of Regularity

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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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Authors and Affiliations

  1. Vakgroep Wiskunde, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussel, België

    Eva Colebunders

  2. Mathematical Sciences, Georgia Southern University, POBOX 8093, Statesboro, GA, 30460, USA

    Frédéric Mynard & William Trott

Authors
  1. Eva Colebunders
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  2. Frédéric Mynard
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  3. William Trott
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Correspondence to Frédéric Mynard.

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Colebunders, E., Mynard, F. & Trott, W. Function Spaces and Contractive Extensions in Approach Theory: The Role of Regularity. Appl Categor Struct 22, 551–563 (2014). https://doi.org/10.1007/s10485-013-9321-z

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  • DOI: https://doi.org/10.1007/s10485-013-9321-z

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