  In the context of generalized descriptive set theory, we systematically
compare and analyze various notions of Polish-like spaces and standard
$\kappa$-Borel spaces for $\kappa$ an uncountable (regular) cardinal satisfying
$\kappa^{<\kappa} = \kappa$. As a result, we obtain a solid framework where one
can develop the theory in full generality. We also provide natural
characterizations of the generalized Cantor and Baire spaces. Some of the
results obtained considerably extend previous work from [Coskey-Schlicht 2016,
Galeotti 2019, Luecke-Schlicht 2015], and answer some questions contained
therein.
