query: Two topology(norm topology and quotient topology) coincident
positive_passages.docid: 124458
positive_passages.text: Quotient of a Banach space $X$ gets quotient topology under standard norm induced from $X$.
negative_passages.docid: 157578
negative_passages.text: perfect map in topology
negative_passages.docid: 130361
negative_passages.text: Basis for a topology with a countable number of sets
negative_passages.docid: 66239
negative_passages.text: Verifying that a certain collection of intervals of $\mathbb R$ forms a topology
negative_passages.docid: 154762
negative_passages.text: Dual space of a finite dimensional normed space
negative_passages.docid: 102485
negative_passages.text: Showing that a topological space is ${\rm T}_1$
negative_passages.docid: 112306
negative_passages.text: Two manifolds $X$ and $Y$ with two bijective continuous functions from $X$ to $Y$ and $Y$ to $X$, but not homeomorphic
negative_passages.docid: 17544
negative_passages.text: another topology multiple choice
negative_passages.docid: 70082
negative_passages.text: Show: Quotient space is homeomorphic to unit sphere
negative_passages.docid: 105996
negative_passages.text: Topology of matrices
negative_passages.docid: 57468
negative_passages.text: Continuous homorphisms between topological groups.
negative_passages.docid: 106298
negative_passages.text: Prove that some topology is not metrizable
negative_passages.docid: 41047
negative_passages.text: Subspace Topology of a subset
negative_passages.docid: 158706
negative_passages.text: How convergence relates to equivalence of norms
negative_passages.docid: 39010
negative_passages.text: Metrization of the cofinite topology
negative_passages.docid: 62128
negative_passages.text: Zariski Topology question
negative_passages.docid: 103923
negative_passages.text: Double orthogonal complement is equal to topological closure