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arXiv · 2007.07955

Metrics on doubles as an inverse semigroup II

Vladimir Manuilov
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Abstract

We have shown recently that, given a metric space $X$, the coarse equivalence classes of metrics on the two copies of $X$ form an inverse semigroup $M(X)$. Here we give several descriptions of the set $E(M(X))$ of idempotents of this inverse semigroup and its Stone dual space $\widehat X$. We also construct $\sigma$-additive measures on $\widehat X$ from finitely additive probability measures on $X$ that vanish on bounded subsets.

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Vladimir Manuilov. 2020-07-15. Metrics on doubles as an inverse semigroup II. https://arxiv.org/abs/2007.07955

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