Topology_Course_Lecture_Notes-McCluskey-McMaster.pdf

(393 KB) Pobierz

23.dvi

the intersection of any two open sets is open and

Denition A topological space is a pair X T consisting of a set X

T T and X T

T of open subsets of X is also called a topology for X

iii Dene T

f X g for any set Xknown as the trivial or antidiscrete topology

Lemma Let X T beatopological space and for each x Xlet N x

iv U N x W N x such that W U

and W N y for each

represented as a union of a subfamily of B

x G T B B such that x B G

Conversely any base B for a topological space X T satises B and B

Denition Let X T be a topological space A family S T is called

S for i k is a base for X T