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
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.