Locally finite

Every point has a finite neighborhood. Equivalently, the space has a basis of finite sets.

Id	If	Then
T218	Discrete	Locally finite
T266	Finite	Locally finite
T292	Anticompact ∧ $k_1$ -space	Locally finite
T293	Locally finite	Anticompact
T307	Locally finite ∧ $T_0$	Scattered
T513	Locally finite	Quasi-sober
T564	Locally finite	Locally countable
T565	Locally finite	Alexandrov
T567	Hereditarily connected ∧ Locally finite	Countable
T647	Locally finite ∧ ¬Empty	Strongly Choquet
T672	Almost discrete ∧ ¬Semiregular	Locally finite
T677	Locally finite	Has a $\sigma$ -locally finite network