query: Proving that the subspace topology only works for subsets of topological spaces
positive_passages.docid: 147793
positive_passages.text: A variation on the induced topology (subspace topology)
negative_passages.docid: 106606
negative_passages.text: How to prove that compact subspaces of the Sorgenfrey line are countable?
negative_passages.docid: 135814
negative_passages.text: Prove certain subsets of $\mathbb R^n$ are subspaces
negative_passages.docid: 121047
negative_passages.text: Proof: Sum of dimension of orthogonal complement and vector subspace
negative_passages.docid: 106298
negative_passages.text: Prove that some topology is not metrizable
negative_passages.docid: 11301
negative_passages.text: Union of two vector subspaces not a subspace?
negative_passages.docid: 134999
negative_passages.text: Writing empty set as union of basis elements for a topology.
negative_passages.docid: 125073
negative_passages.text: Finite-dimensional subspaces of normed vector spaces are direct summands
negative_passages.docid: 481
negative_passages.text: Can compact sets completey determine a topology?
negative_passages.docid: 79213
negative_passages.text: Proof about a Topological space being arc connect
negative_passages.docid: 42913
negative_passages.text: Equivalence of the definition of the Subbasis of a Topology
negative_passages.docid: 6547
negative_passages.text: Given $3$-dimensional subspaces $V, W \subset \Bbb R^5$, there is a nonzero vector in $V \cap W$
negative_passages.docid: 72190
negative_passages.text: Topological proof on discrete topology where $X$ is infinite
negative_passages.docid: 40071
negative_passages.text: What is the cardinality of the set of all topologies on $\mathbb{R}$?
negative_passages.docid: 150796
negative_passages.text: Subspace topology and order topology (2)
negative_passages.docid: 130361
negative_passages.text: Basis for a topology with a countable number of sets
negative_passages.docid: 146143
negative_passages.text: Question about proof that finite-dimensional subspaces of normed vector spaces are direct summands