${\omega }^{\omega }$-Dominated function spaces and ${\omega }^{\omega }$-bases in free objects of Topological Algebra

Abstract

A topological space $X$ is defined to have an ${\omega }^{\omega }$-base if at each point $x\in X$ the space $X$ has a neighborhood base $(U_{\alpha }[x]{)}_{\alpha \in {\omega }^{\omega }}$ such that $U_{\beta }[x]\subset U_{\alpha }[x]$ for all $\alpha \le \beta$ in ${\omega }^{\omega }$. We characterize topological and uniform spaces whose free (locally convex) topological vector spaces or free (Abelian or Boolean) topological groups have ${\omega }^{\omega }$-bases.

30 pages (some references are updated). arXiv admin note: text overlap with arXiv:1606.01967

References in corpus (1)

• The character of topological groups, via bounded systems, Pontryagin--van Kampen duality and pcf theory