Category:Quotient Topological Vector Space is Hausdorff iff Linear Subspace is Closed
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This category contains pages concerning Quotient Topological Vector Space is Hausdorff iff Linear Subspace is Closed:
Let $\GF \in \set {\R, \C}$.
Let $\struct {X, \tau}$ be a topological vector space over $\GF$.
Let $N$ be a linear subspace of $X$.
Let $X/N$ be the quotient vector space of $X$ modulo $N$.
Let $\tau_N$ be the quotient topology on $X/N$.
Then $\struct {X/N, \tau_N}$ is Hausdorff if and only if:
- $N$ is a closed linear subspace.
Pages in category "Quotient Topological Vector Space is Hausdorff iff Linear Subspace is Closed"
The following 3 pages are in this category, out of 3 total.