Consider the open ordinal space $[0,\Omega)$, where $\Omega$ is the first uncountable ordinal. Can I say that every subset of $[0,\Omega)$ is $G_\delta$? If yes, does this imply that $[0,\Omega)$ is ...
Denote by $ZF^\times$ the theory of $ZF$ without the axiom of infinity. We know that $V_\omega$, the set of all hereditarily finite sets in a model of $ZF$, is a model of $ZF^\times$. We further know ...
According to http://en.wikipedia.org/wiki/Analytical_hierarchy The set of all natural numbers which are indices of computable ordinals is a $\Pi^1_1$ set which is not $\Sigma^1_1$. However, "the ...
Given a set $P$ of real numbers, its derived set is the set of all accumulation points - $a\in P^\prime$ if every open set containing $a$ also contains an infinite number of points from $P$ ...
I am trying to get a better feel for the topology of ordinals and just received a great answer to this question where the Cantor-Bendixson rank and degree turn out to be a complete homeomorphism ...
I heard at some point (without seeing a proof) that every countable, compact space $X$ is homeomorphic to a countable successor ordinal with the usual order topology. Is this true? Perhaps someone can ...