# Questions tagged [polish-spaces]

For questions involving Polish spaces, that is, separable and completely metrizable topological spaces.

108 questions
Filter by
Sorted by
Tagged with
109 views

• 743
70 views

1 vote
361 views

### Suslin sets and projections

In a paper I am reading about optimal transport (we are in a proper metric space, https://arxiv.org/pdf/2004.08934.pdf, page 49 at the end), there's written in a proof "Being (this set) the ...
207 views

### Projection of an Analytic Set is Analytic

Let $\mathscr{I}$ be the family of all finite sequences in $\mathbb{N}$ and let us use Greek letters $\alpha,\beta\ldots$ to denote elements of $\mathscr{I}$. Given a paved space $(X,\mathscr{X})$, a ...
• 1,045
1 vote
67 views

### $(X, \mathcal{T})$ Polish and $F \subseteq X$ closed $\implies$ topology generated by $\mathcal{T} \cup \{ F \}$ is Polish

I am trying to understand the proof of this statement (Kechris, Classical Descriptive Set Theory, p. 82). (13.2) Lemma. Let $(X, \mathcal{T})$ be Polish and $F \subseteq X$ closed. Let $\mathcal{T}_F$...
• 219
90 views

### Second-countable, analytic, completely Baire spaces

First a few definitions. A topological space $(X,\tau)$ is said to be: a Polish space if it is separable and completely metrizable. Analytic, if there exists a surjective continuous map from a (Borel ...
• 2,601