Property P000136

Anticompact

Also known as: Compact subsets are finite

Every compact subset of the space is finite.

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• Theorems
• Spaces
• References

Id	If	Then
T22	Anticompact ∧ Countable	Has a countable $k$-network
T222	Countable sets are discrete	Anticompact
T291	Anticompact ∧ Countable	Hemicompact
T292	Anticompact ∧ $k_1$-space	Locally finite
T293	Locally finite	Anticompact
T303	Anticompact ∧ Compact	Finite
T304	Anticompact ∧ $\sigma$-compact	Countable
T318	Anticompact ∧ $T_1$	$k_1$-Hausdorff
T377	Anticompact ∧ $\omega$-Lindelöf	$k$-Lindelöf
T378	Anticompact ∧ $\omega$-Menger	$k$-Menger
T379	Anticompact ∧ Strategically Rothberger	Strategically $k$-Rothberger
T380	Anticompact ∧ $\omega$-Rothberger	$k$-Rothberger
T413	Anticompact ∧ $T_1$	Sequentially discrete
T568	Door ∧ Hyperconnected	Anticompact
T678	Anticompact ∧ Has a $\sigma$-locally finite network	Has a $\sigma$-locally finite $k$-network
T700	Door ∧ ¬Anticompact	Almost discrete