New posts in Descriptive Set Theory

Continuous open metrizable image of a Polish space is Polish

There is a $\Sigma^1_1$ universal set and this is not Borel. Where did we use the axiom of choice?

Does every uncountable Borel subset of $\mathbb R$ contains a perfect subset？

Does every null set have a superset which is an $F_{\sigma}$ null set?

Is it possible to divide the real line into two disjoint totally disconnected spaces of equal cardinality?

A $G_δ$ subset of $2^ω$ that is homeomorphic to $ω^ω$

Reference request, Descriptive set theory

Why do we study Polish spaces?

Bijection between closed uncountable subset of $\Bbb R$ and $\Bbb R$.

Examples of uncountable sets with zero Lebesgue measure