Page 1 of 1

Irreducible

Posted: Sun Jun 19, 2016 12:00 pm
by Papapetros Vaggelis
A topological space is said to be irreducible if it is not the union of two proper closed subsets.

For the topological space \(\displaystyle{\left(X,\mathbb{T}\right)}\), the following are equivalent :

1. The topological space \(\displaystyle{\left(X,\mathbb{T}\right)}\) is irreducible.

2. Every pair of nonempty open subsets has nonempty intersection.

3. Every nonempty open subset is dense.