Locally pseudometrizable

Every point has a neighborhood that is Pseudometrizable.

$X$ is Locally pseudometrizable iff its Kolmogorov quotient $\text{Kol}(X)$ is Locally metrizable.

Id	If	Then
T57	Locally pseudometrizable	First countable
T202	Locally pseudometrizable ∧ $R_1$ ∧ Paracompact	Pseudometrizable
T326	Pseudometrizable	Locally pseudometrizable
T327	Locally metrizable	Locally pseudometrizable
T330	Locally pseudometrizable	$R_0$
T331	Locally pseudometrizable ∧ $T_0$	Locally metrizable
T521	Locally pseudometrizable	Quasi-sober
T689	Locally countable ∧ Locally pseudometrizable ∧ Locally connected	Partition topology