query: A normed space is locally compact iff it is finite dimensional
positive_passages.docid: 155621
positive_passages.text: Finiteness of the dimension of a normed space and compactness
negative_passages.docid: 34173
negative_passages.text: Banach spaces and their unit sphere
negative_passages.docid: 143484
negative_passages.text: A separable locally compact metric space is compact iff all of its homeomorphic metric spaces are bounded
negative_passages.docid: 49087
negative_passages.text: Show that a norm on an inner product space satisfies parallelogram law.
negative_passages.docid: 99300
negative_passages.text: Prove if $W \subset V$ is a subspace such that $T(W)\subset W$, then $V/W$ is finite-dimensional.
negative_passages.docid: 146146
negative_passages.text: Proof that a closed subset of a compact space is a compact space
negative_passages.docid: 147213
negative_passages.text: Prove that finite unions of compact sets are compact
negative_passages.docid: 94485
negative_passages.text: Limit point compactness implies compactness.
negative_passages.docid: 45252
negative_passages.text: "Every linear mapping on a finite dimensional space is continuous"
negative_passages.docid: 15839
negative_passages.text: equivalent norms in Banach spaces of infinite dimension
negative_passages.docid: 144112
negative_passages.text: Show that $c_0$ is a Banach space with the norm $\rVert \cdot \lVert_\infty$
negative_passages.docid: 127522
negative_passages.text: Space $\mathcal{L}^p(X, \Sigma, \mu)$ is separable iff $(\Sigma, \rho_\Delta)$ is separable
negative_passages.docid: 14509
negative_passages.text: Contraction Map on Compact Normed Space has a Fixed Point
negative_passages.docid: 132869
negative_passages.text: Show that any bounded linear functional on a normed linear space is continuous
negative_passages.docid: 125073
negative_passages.text: Finite-dimensional subspaces of normed vector spaces are direct summands
negative_passages.docid: 10383
negative_passages.text: The $ l^{\infty} $-norm is equal to the limit of the $ l^{p} $-norms.
negative_passages.docid: 158498
negative_passages.text: $A\subset \mathbb{R}$ with more than one element and $A/ \{a\}$ is compact for a fixed $a\in A$