Examples
Most topological spaces commonly studied in mathematics are compactly generated.
- Every compact space is compactly generated.
- Every locally compact space is compactly generated.
- Every first-countable space is compactly generated.
- Topological manifolds are locally compact Hausdorff and therefore compactly generated Hausdorff.
- Metric spaces are first-countable and therefore compactly generated Hausdorff.
- Every CW complex is compactly generated Hausdorff.
Read more about this topic: Compactly Generated Space
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