Definition:Irreducible Subset (Topology)
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Definition
Let $T = \struct {S, \tau}$ be a topological space.
Let $A$ be a subset of $S$.
Then $A$ is irreducible (subset) if and only if
- $A$ is non-empty and closed and for all closed subsets $B, C$ of $S$: $A = B \cup C \implies A = B$ or $A = C$
Sources
- Mizar article YELLOW_8:def 3