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Results tagged with infinite-dimensional-manifolds
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user 22277
9
votes
Accepted
Is the strong Whitney topology connected?
No. It is not a connected space. We can in fact describe the connected components of this space quite easily. Let $\simeq$ be the equivalence relation on $C$ where $f\simeq g$ iff $f-g$ has compact su …
6
votes
Dimension of An Ultraproduct Field as a Vector Space over Another Ultraproduct Field
Let $B$ be a basis for $K$ over $F$. Let $B^{*}$ denote the ultrapower $B^{X}/\mathcal{U}$. Then $F^{*}\subseteq B^{*}\subseteq K^{*}$. Since the statement "$B$ is linearly independent over $F$" is a …