Irreducible

General Topology
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Papapetros Vaggelis
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Joined: Mon Nov 09, 2015 1:52 pm

Irreducible

#1

Post 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.
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