# Completely metrizable implies Baire

This article gives the statement and possibly, proof, of an implication relation between two topological space properties. That is, it states that every topological space satisfying the first topological space property (i.e., completely metrizable space) must also satisfy the second topological space property (i.e., Baire space)

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## Contents

## Statement

If a topological space is **completely metrizable** (i.e. it can be given the structure of a complete metric space) then it is a Baire space.

## Definitions used

### Completely metrizable space

`Further information: Completely metrizable space`

### Baire space

`Further information: Baire space`