Function spaces and contractive extensions in Approach Theory: The role of regularity
| Autor: | Colebunders, Eva, Mynard, Frédéric, Trott, Will |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Applied Categorical Structures 22(3) Page 551-563, 2014 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s10485-013-9321-z |
| Popis: | 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. Comment: previous version had an error, fixed here with a new definition of strictness |
| Databáze: | arXiv |
| Externí odkaz: |
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