1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Basis for a topology?

  1. May 27, 2007 #1
    1. The problem statement, all variables and given/known data
    Does a basis exist for all sets with a topology? In other words do all topological spaces with topology T contain a basis for T?
  2. jcsd
  3. May 27, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper

    Of course. T itself is always a basis for T. In general, just as with vector spaces, there is no single unique basis for a given topology, but there is always a basis for it. The only time a topology might have a unique basis is if it's the indiscrete topology, or something like that.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook