Let $T = (X, \mathcal{T})$ be a D2299: Polish topological space.

Then $T$ is a D501: First-countable topological space.

Result R4010
on D501: First-countable topological space

*Subresult of R610: Metrisable topological space is first-countable*

Polish space is first-countable

Formulation 0

Let $T = (X, \mathcal{T})$ be a D2299: Polish topological space.

Then $T$ is a D501: First-countable topological space.

Proofs

Let $T = (X, \mathcal{T})$ be a D2299: Polish topological space.

This result is a particular case of R610: Metrisable topological space is first-countable. $\square$