Chapter 2.13: Basis for a Topology Flashcards

1
Q

Definition: a “Basis” for a topology

A

B is a basis for a topology T on X if

(1) For each x in X, there is at least one basis element in B containing x
(2) If x is contained in two basis elements B1 and B2 in B, then there is another element of the basis B3 such that x is in B3 and B3 is a subset of the intersection of B1 and B2

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2
Q

Explain how a basis B generates a topology T

A

A basis B defines a topology T as follows: as set U is open (in T) if for each x in U there is a basis element B0 in B such that x is in B0 and B0 is a subset of U.

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