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arXiv · 1212.6398

Function spaces and contractive extensions in Approach Theory: The role of regularity

Eva Colebunders·Frédéric Mynard·Will Trott
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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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Eva Colebunders, Frédéric Mynard, Will Trott. 2014-10-29. Function spaces and contractive extensions in Approach Theory: The role of regularity. https://doi.org/10.1007/s10485-013-9321-z

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