Function spaces and contractive extensions in Approach Theory: The role of regularity
General Topology
2014-10-31 v3
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.
Keywords
Cite
@article{arxiv.1212.6398,
title = {Function spaces and contractive extensions in Approach Theory: The role of regularity},
author = {Eva Colebunders and Frédéric Mynard and Will Trott},
journal= {arXiv preprint arXiv:1212.6398},
year = {2014}
}
Comments
previous version had an error, fixed here with a new definition of strictness