Category:Definitions/Sober Spaces
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This category contains definitions related to Sober Spaces.
Related results can be found in Category:Sober Spaces.
Let $T = \struct {S, \tau}$ be a topological space.
Definition 1
Then $T$ is a sober space if and only if:
- each closed irreducible subspace of $T$ has a unique generic point.
Definition 2
Then $T$ is a sober space if and only if:
- for every meet-irreducible open set $U \ne S$ there exists a unique $x \in S$ such that:
- $U = S \setminus \set x^-$
- where $\set x^-$ denotes the closure of $\set x$.
Pages in category "Definitions/Sober Spaces"
The following 3 pages are in this category, out of 3 total.