Point set topology problems
In algebraic topology, many point-set topology problems arise. For example, the product of quotient maps need not be a quotient map; the smash product may not be associative; the canonical map $Z^{X\times Y}\cong(Z^Y)^X$ is not necessarily a homeomorphism... It seems that many authors chooses to stay in the category of compactly generated (weak Hausdorff) spaces to remedy this. For example, in Chapter 5 of Algebraic Topology by J. P. May, he introduces this concept and states without proof some basic properties, and then he assumes all topological spaces are compactly generated in the remainder of the book. On the other hand, some authors do not assume this. Then some restrictions are necessary. In this context local compactness frequently crops up. Here are my questions:
Thanks for any advice! https://doi.org/10.1142/9789812385406_0005Cited by:0 Abstract: Let A and B be connected subspaces of a topological space X, such that A ∩ |