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quasicompact

• A space \(X\in {\mathsf{Top}}\) is quasicompact iff every open cover admits a finite subcover.

• A morphism \(f\in {\mathsf{Sch}}(X, Y)\) is quasicompact iff \(Y\) admits an affine open cover \({\mathcal{V}}\rightrightarrows Y\) with \(f^{-1}({\mathcal{V}})\) all quasicompact spaces.

• A morphism is quasicompact if it sends quasicompact sets to quasicompact sets.