query: Show that it is not a Banach Space
positive_passages.docid: 154796
positive_passages.text: Completeness of sequence of reals with finitely many nonzero terms
negative_passages.docid: 11259
negative_passages.text: Prove $R\times S$ is not an integral domain
negative_passages.docid: 62428
negative_passages.text: How to prove this inequality in Banach space?
negative_passages.docid: 80735
negative_passages.text: Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
negative_passages.docid: 67383
negative_passages.text: Prove that $G'$ is not planar.
negative_passages.docid: 109632
negative_passages.text: Show reflexive normed vector space is a Banach space
negative_passages.docid: 115272
negative_passages.text: Showing that projections $\mathbb{R}^2 \to \mathbb{R}$ are not closed
negative_passages.docid: 139176
negative_passages.text: The real line is not homeomorphic to any non-trivial product space
negative_passages.docid: 104881
negative_passages.text: Showing that two Banach spaces are homeomorphic when their dimensions are equal.
negative_passages.docid: 14516
negative_passages.text: The space of continuous functions $C([0,1])$ is not complete in the $L^2$ norm
negative_passages.docid: 68153
negative_passages.text: How to show that $L^p$ spaces are nested?
negative_passages.docid: 96717
negative_passages.text: Hahn-Banach Theorem for separable spaces without Zorn's Lemma
negative_passages.docid: 99726
negative_passages.text: Proving that a function is not a contraction
negative_passages.docid: 7345
negative_passages.text: Is $C[0,1]$ a Banach space for the $L^1$ norm?
negative_passages.docid: 46326
negative_passages.text: The space $C[a,b]$ with $\|f\|:=\int_a^b |f(x)|d(x)$ is a normed space but not a Banach space
negative_passages.docid: 125277
negative_passages.text: Image of the tensor product of strict maps of Banach spaces
negative_passages.docid: 29653
negative_passages.text: Show that $xy=0$ is a variety but not a manifold