characterization of compactly generated space
Clearly, for such spaces . With this we have the following theorem.
Theorem. Let be a Hausdorff space. Then the following conditions are equivalent.
i) is compactly generated
iii) For every topological space we have .
iv) is an image of a locally compact space under a quotient mapping.
Remark. It follows easily from this that if there is a quotient mapping which maps a compactly generated space onto a Hausdorff space then is compactly generated.
|Title||characterization of compactly generated space|
|Date of creation||2013-03-22 19:10:04|
|Last modified on||2013-03-22 19:10:04|
|Last modified by||karstenb (16623)|