Easy question regarding the basis for a topology

  • Thread starter christian1357
  • Start date
  • #1
christian1357

Main Question or Discussion Point

Hello, I know that given a set $X$ and a topology $T$ on $X$ that a basis $B$ for $T$ is a collection of open sets of $T$ such that every open set of $T$ is the Union of sets in $B$. My question is: does taking the set of all Unions of sets in $B$ give exactly the topology $T$ ?
 

Answers and Replies

  • #2
mathman
Science Advisor
7,766
417
Yes - directly from the definition. A topology is defined by open sets. The set of all open sets is closed under all unions and finite intersections, so adding more open sets to the basis doesn't change the topology.
 

Related Threads for: Easy question regarding the basis for a topology

  • Last Post
Replies
2
Views
2K
Replies
5
Views
499
Replies
3
Views
2K
Replies
12
Views
2K
  • Last Post
2
Replies
29
Views
4K
  • Last Post
Replies
8
Views
3K
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
20
Views
4K
Top