Irreducible
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Irreducible
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.
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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