query: Finite Dimensional Vector Spaces and Completeness
positive_passages.docid: 19415
positive_passages.text: Proof that every finite dimensional normed vector space is complete
negative_passages.docid: 154324
negative_passages.text: preservation of completeness under homeomorphism
negative_passages.docid: 84830
negative_passages.text: Vector space of infinite sequences in $\Bbb R$
negative_passages.docid: 41520
negative_passages.text: Prove that $L(V,W)$ forms a vector space
negative_passages.docid: 17
negative_passages.text: First Order Language for vector spaces over fields
negative_passages.docid: 81379
negative_passages.text: Any two bases of a finite dimensional vector space must have the same number of elements.
negative_passages.docid: 98759
negative_passages.text: Proof of "Dual normed vector space is complete"
negative_passages.docid: 110654
negative_passages.text: Vector Spaces and AC
negative_passages.docid: 17748
negative_passages.text: Is there a quick proof as to why the vector space of $\mathbb{R}$ over $\mathbb{Q}$ is infinite-dimensional?
negative_passages.docid: 83360
negative_passages.text: The completion of a separable inner product space is a separable Hilbert space
negative_passages.docid: 146143
negative_passages.text: Question about proof that finite-dimensional subspaces of normed vector spaces are direct summands
negative_passages.docid: 81423
negative_passages.text: Completeness and Topological Equivalence
negative_passages.docid: 37119
negative_passages.text: Determine Which of the following Sets is a Vector Space
negative_passages.docid: 122121
negative_passages.text: Is there a vector space that cannot be an inner product space?
negative_passages.docid: 33642
negative_passages.text: Finite dimensional subspace of $C([0,1])$
negative_passages.docid: 143517
negative_passages.text: Isomorphisms Between a Finite-Dimensional Vector Space and its Dual
negative_passages.docid: 86362
negative_passages.text: Cyclic vectors in a real vector space