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 must also satisfy the second topological space property
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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