## New answers tagged infinite-games

6
votes

### Embeds in a topological W-group, or a W-space that embeds in a topological group?

Or, you can embed $X$ into a Tychonoff cube $[0,1]^\kappa$, where $\kappa$ is the weight of $X$, say.
The Tychonoff cube embeds in the corresponding power of the unit circle, say by embedding $[0,1]$ ...

6
votes

Accepted

### Embeds in a topological W-group, or a W-space that embeds in a topological group?

No, every Tychonoff space $X$ (so in particular every compact Hausdorff space) embeds (as a closed subspace) in $F(X)$, the free topological group over $X$.
See chapter 7 of Topological groups and ...

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