Compactly continuous map
A map $f$ of topological spaces $X \rightarrow Y$ with the property that the restriction of $f$ to any compact subspace of $X$ is continuous. Clearly any continuous map is compactly continuous, and the converse holds if $X$ is a locally compact space. The composite of compactly continuous maps is again compactly continuous.
- Francis Borceux, "Handbook of Categorical Algebra: Volume 2, Categories and Structures", Encyclopedia of Mathematics and its Applications, Cambridge University Press (1994) ISBN 0-521-44179-X Zbl 1143.18002
- R. Brown, "Function spaces and product topologies" Quart. J. Math. 2 (1964) pp. 238–250. Zbl 0126.38503
Compactly continuous map. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Compactly_continuous_map&oldid=51461