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Theorem 3.1. Let (X,T) be a topological space, and let B be a collection of subsets of X. Then B is a basis for T if and only if (1) B C J, and (2) for each set U in F and point p in U there is a set V in B such that p e V C U.

Theorem 3.1. Let (X,T) be a topological space, and let B be a collection of subsets of X. Then B is a basis for T if and only if (1) B C J, and (2) for each set U in F and point p in U there is a set V in B such that p e V C U.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Could you explain how to show theorem3.1 in detail? Thank you!

Theorem 3.1. Let (X,T) be a topological space, and let B be a collection of subsets of X. Then B is a basis for T if and only if (1) B C J, and (2) for each set U in F and point p in U there is a set V in B such that p e V C U.
Transcribed Image Text:Theorem 3.1. Let (X,T) be a topological space, and let B be a collection of subsets of X. Then B is a basis for T if and only if (1) B C J, and (2) for each set U in F and point p in U there is a set V in B such that p e V C U.
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