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Let (M; d) be a metric space. Show that the set {B(x; 1=n); x ∈ M; n ∈ N*} is a Basis for the metric topology.

Let (M; d) be a metric space. Show that the set {B(x; 1=n); x ∈ M; n ∈ N*} is a Basis for the metric topology.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 24CM
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Let (M; d) be a metric space. Show that the set {B(x; 1=n); x ∈ M; n ∈ N*} is a Basis for the metric topology.

 

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