# Bases for topologies

• March 7th 2010, 07:23 AM
Debor
Bases for topologies
Hello i need yours help!!

Show that the class of closed intervals [a,b], where a and b are rational and a<b, is not a base for a topology on the real line R
• March 7th 2010, 07:55 AM
Opalg
Quote:

Originally Posted by Debor
Hello i need yours help!!

Show that the class of closed intervals [a,b], where a and b are rational and a<b, is not a base for a topology on the real line R

Suppose that a<b<c, and consider the intersection $[a,b]\cap[b,c]$.
• March 7th 2010, 08:42 PM
Drexel28
Quote:

Originally Posted by Debor
Hello i need yours help!!

Show that the class of closed intervals [a,b], where a and b are rational and a<b, is not a base for a topology on the real line R

How do you define base? What topology?