# $\omega^\omega$-Dominated function spaces and $\omega^\omega$-bases in free objects of Topological Algebra Academic Article

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• Overview
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### abstract

• 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.

### publication date

• November 19, 2016