Definition:Irreducible Subset
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Definition
Let $T = \struct {S, \tau}$ be a topological space.
Let $A \subseteq S$ be non-empty.
Let $\tau_A$ be the subspace topology on $A$ induced by $\tau$.
Then $A$ is an irreducible subset (of $S$ in $T$) if and only if $\struct {A, \tau_A}$ is an irreducible space.
Sources
- 1977: Robin Hartshorne: Algebraic Geometry $\text {I}.1:$ Affine Varieties, Definition on Page 3