Category:Definitions/Meet-Irreducible Open Sets

This category contains definitions related to Meet-Irreducible Open Sets.
Related results can be found in Category:Meet-Irreducible Open Sets.

Let $\struct {S, \tau}$ be a topological space.

Let $W \in \tau$.

Then $W$ is a meet-irreducible open set if and only if:

$W$ is meet-irreducible in the frame $\struct {\tau, \subseteq}$

That is, $W$ is a meet-irreducible open set if and only if:

$\forall U, V \in \tau : \paren {U \cap V \subseteq W \implies U \subseteq W \text { or } V \subseteq W}$