Suppose you are given a set X and a collection B of subsets of X. Under...
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Suppose you are given a set X and a collection B of subsets of X. Under what circumstances is there a topology for which B is a basis? Note how this question is different from the question that motivated Theorem 3.1. That theorem describes when a collection of sets forms a basis for a given topology. The next theorem describes when a collection of sets forms a basis for some topology on X. Suppose you are given a set X and a collection B of subsets of X. Under what circumstances is there a topology for which B is a basis? Note how this question is different from the question that motivated Theorem 3.1. That theorem describes when a collection of sets forms a basis for a given topology. The next theorem describes when a collection of sets forms a basis for some topology on X.
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To determine under what circumstances there exists a topology for which a given collection B is a basis we need to ensure that the collection B satisf... View the full answer
Related Book For
Introduction to Data Mining
ISBN: 978-0321321367
1st edition
Authors: Pang Ning Tan, Michael Steinbach, Vipin Kumar
Posted Date:
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