query: Prove that:$(P,\Vert\cdot\Vert)$ is not a Banach space.
positive_passages.docid: 28731
positive_passages.text: Banach space in functional analysis
negative_passages.docid: 71848
negative_passages.text: Show that $(L^{p},\|\|_{p})$ is a Banach space.
negative_passages.docid: 10540
negative_passages.text: Prove $\vdash \neg(\square F\land p)$ in $KD$
negative_passages.docid: 28819
negative_passages.text: A union of two subspaces not equal to the vector space.
negative_passages.docid: 17067
negative_passages.text: To prove that $(\mathbb{P(N)},d)$ is a metric space
negative_passages.docid: 19294
negative_passages.text: ‎If ‎‎$‎X$ is an infinite-dimensional Banach space and ‎‎$‎‎u‎\in ‎B(X)‎$ ,then $\bigcap_{v\in K(X)}\sigma(u+v) =\cdots$
negative_passages.docid: 81229
negative_passages.text: Show that $(C([a,b]),\|{\cdot}\|_2)$ is not a complete normed vector space
negative_passages.docid: 76572
negative_passages.text: What facts about the weak topology fail in spaces that aren't Banach?
negative_passages.docid: 25050
negative_passages.text: To prove that $(F,+)$ and $(F-\{0\},\cdot)$ are not isomorphic as groups.
negative_passages.docid: 35569
negative_passages.text: Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
negative_passages.docid: 139272
negative_passages.text: On the norm of a quotient of a Banach space.
negative_passages.docid: 126744
negative_passages.text: Is any Banach space a dual space?
negative_passages.docid: 99726
negative_passages.text: Proving that a function is not a contraction
negative_passages.docid: 132713
negative_passages.text: The space $c_0$ of sequences that converge to 0 is not reflexive
negative_passages.docid: 96717
negative_passages.text: Hahn-Banach Theorem for separable spaces without Zorn's Lemma
negative_passages.docid: 34173
negative_passages.text: Banach spaces and their unit sphere
negative_passages.docid: 44738
negative_passages.text: Compact operators on an infinite dimensional Banach space cannot be surjective