nLab
convenient category of topological spaces

The term convenient category of topological spaces is used for a cartesian closed category of topological spaces. These are examples of nice categories of spaces.

One example is the category of compactly generated spaces.

References

• Ronnie Brown, Function spaces and product topologies, Quart. J. Math. (2) 15 (1964), 238–250.
• Norman Steenrod?, A convenient category of topological spaces, Michigan Math. J. 14 (1967) 133–152, project euclid
• Booth, P.; Tillotson, J., Monoidal closed, Cartesian closed and convenient categories of topological spaces. Pacific J. Math. 88 (1980), no. 1, 35–53.