query: Prove that infinite intersection of subspaces is a subspace.
positive_passages.docid: 150135
positive_passages.text: The intersection of an infinite number of subspaces is a subspace
negative_passages.docid: 66283
negative_passages.text: Let V be a vector space. If every subspace of V is T-invariant, prove that there exist a scalar multiple c such that T=c1v
negative_passages.docid: 128730
negative_passages.text: Open subspaces of locally compact Hausdorff spaces are locally compact
negative_passages.docid: 121047
negative_passages.text: Proof: Sum of dimension of orthogonal complement and vector subspace
negative_passages.docid: 14713
negative_passages.text: $X=(-\infty,0]\cup\left\{{1\over n}:n\in\mathbb N\right\}$ with subspace topology Then
negative_passages.docid: 87327
negative_passages.text: Unions and intersections: $(A \cup B = A ∪ C) \land (A \cap B = A ∩ C) \implies B = C.$
negative_passages.docid: 17495
negative_passages.text: Show that the vector space of all continuous real-valued functions is infinite-dimensional
negative_passages.docid: 53261
negative_passages.text: Show that Pn is an (n+1)-dimensional subspace
negative_passages.docid: 74311
negative_passages.text: Proving that the Intersection of any Collection of Compact Sets is Compact
negative_passages.docid: 130156
negative_passages.text: Image of the union and intersection of sets.
negative_passages.docid: 16654
negative_passages.text: Unions and Intersections of Open Sets are Open
negative_passages.docid: 4319
negative_passages.text: Vector space can be written as direct sum of subspaces
negative_passages.docid: 15576
negative_passages.text: Addition of two subspaces
negative_passages.docid: 74465
negative_passages.text: One-dimensional vector space and it's subspaces
negative_passages.docid: 92291
negative_passages.text: $U_1, U_2, ..., U_k$ subspaces of linear space $X$ with same dimensions, prove $X=U_1\oplus V=U_2\oplus V=...=U_k\oplus V$
negative_passages.docid: 79061
negative_passages.text: show that {$(x_1,x_2,x_3,x_4)\in\mathbb{F}^4$:$x_3=5x_4+b$} is a subspace
negative_passages.docid: 65494
negative_passages.text: Proper subspaces of $ R^n $