subspace | product | image | metric | compact Hausdorff | |
T0 | Yes | Yes | Yes | ||
T1 | Yes | Yes | |||
T2 | Yes | Yes | |||
regular | Yes latex | Yes | |||
completely regular | Yes latex | Yes | |||
normal | Yes | ||||
subspace | product | image | metric | compact Hausdorff | |
connected | counterexample latex | yes | |||
locally connected | Open | ||||
path connected | |||||
locally path connected | |||||
subspace | product | image | metric | compact Hausdorff | |
compact | counterexample latex sometimes latex | yes | Yes | ||
locally compact | Yes latex | ||||
limit point compact | answer answer latex | ||||
sequentially compact | |||||
Lindelof | yes latex | ||||
locally compact Hausdorff | Yes latex | ||||
subspace | product | image | metric | compact Hausdorff | |
2nd countable | Yes latex | ||||
1rst countable | |||||
separable | not necessarily, closed yes, open no latex yes latex | ||||
metrizable | yes | ||||
locally metrizable |