All Questions

Let $Q$ be a locally compact Hausdorff space and $E$ be a Banach space. Let $C(Q)$ be the collection of all real-valued continuous functions on $Q$ and $C_b(Q,E)$ be the collection of all $E$-valued ...

The axiom Near Coherence of Filters (NCF) is known to be independent of ZFC. Axiom (NCF I): For any two free ultrafilters $\mathcal D$ and $\mathcal E$ on $\mathbb N$, there exist finite-to-one ...

It is known that in general convergence by sequences is not enough to account for all points in $\beta X \setminus X$, where $\beta X$ refers to the Stone-Cech compactification of a topological space $...

I am currently attending a course where we are now covering the Stone-Cech compactification. Today we proved in some detail that extensions of bounded smooth functions on $\mathbb{R}^n$ to $\beta\...

I am trying to see what is known about uniform density of function spaces in $C(\mathbb{R}^n)$ or $C_b(\mathbb{R}^n)$ (bounded continuous functions on $\mathbb{R}^n$). By uniform density, I mean ...

Is the following statement true, and if it is, does someone have a reference? Let $X$ be a compact (i.e., compact and Hausdorff) topological space. Then the Gleason space (=Iliadis absolute, =...