query: Topology induced by equivalent norms
positive_passages.docid: 151161
positive_passages.text: norms on vector space are equivalent iff they have same topology
negative_passages.docid: 84104
negative_passages.text: Definition of neighborhood and open set in topology
negative_passages.docid: 65840
negative_passages.text: Norm induced by metric
negative_passages.docid: 111001
negative_passages.text: Does weak topology preserve topological vector space structure?
negative_passages.docid: 148804
negative_passages.text: Norm-Euclidean rings?
negative_passages.docid: 151581
negative_passages.text: Prerequisite for Milnor Topology from a Differential Viewpoint
negative_passages.docid: 156922
negative_passages.text: Proving convergence iff projection converges in product topology
negative_passages.docid: 130361
negative_passages.text: Basis for a topology with a countable number of sets
negative_passages.docid: 150287
negative_passages.text: Spectral radii and norms of similar elements in a C*-algebra: $\|bab^{-1}\|<1$ if $b=(\sum_{n=0}^\infty (a^*)^n a^n)^{1/2}$
negative_passages.docid: 135025
negative_passages.text: Axiomatization of a Topology using the Boundary
negative_passages.docid: 78344
negative_passages.text: Nonconstant linear functional on a topological vector space is an open mapping
negative_passages.docid: 51871
negative_passages.text: Characterization of Topology
negative_passages.docid: 52388
negative_passages.text: The equivalence of open-set definition of continuous mappings to the $\epsilon-\delta$ definition
negative_passages.docid: 155621
negative_passages.text: Finiteness of the dimension of a normed space and compactness
negative_passages.docid: 97914
negative_passages.text: Contractive mapping on compact space
negative_passages.docid: 114856
negative_passages.text: Universal property of initial topology
negative_passages.docid: 150987
negative_passages.text: Showing that the product and metric topology on $\mathbb{R}^n$ are equivalent