# Fragmentability of groups and metric-valued function spaces

Moors, Warren

### Abstract

Let *TeX Embedding failed!* be a topological space and let *TeX Embedding failed!* be a metric defined on *TeX Embedding failed!*. We shall say that *TeX Embedding failed!* is *TeX Embedding failed!* *TeX Embedding failed!* if whenever *TeX Embedding failed!* and *TeX Embedding failed!* is a nonempty subset of *TeX Embedding failed!* there is a *TeX Embedding failed!*-open set *TeX Embedding failed!* such that *TeX Embedding failed!* and *TeX Embedding failed!*. In this talk we will consider the notion of fragmentability, and its generalisation *TeX Embedding failed!*-fragmentability, in the setting of topological groups and metric-valued function spaces. The primary tool used is that of topological games.

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