Co-Blumberg spaces. (English) Zbl 0603.54015
A pair (X,Y) of topological spaces is said to be a Blumberg pair (”BP”) if for every \(f: X\to Y\), there exists a dense subset D of X such that \(f| D\) is continuous. X is a Blumberg space if (X,R) is BP, where R denotes the reals. Y is co-Blumberg if (R,Y) is BP. We survey the literature concerning the relationships between Blumberg spaces and Baire spaces and then study the relationships between co-Blumberg spaces and separability properties.
MSC:
| 54C30 | Real-valued functions in general topology |
| 26A15 | Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable |
| 54E52 | Baire category, Baire spaces |
References:
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