supercompact

Definition

• A space with a binary closed subbase is called supercompact.

Definition 2

• A space is called supercompact if every open cover has a singleton subcover.

Remark

Definition2

• [Hofmann] Such a subspace of a topological space is also called singly generated or monogenerated.

Reference

Definition

• J. van Mill and E. Wattel, An external characterization of spaces which admit binary normal subbase, Amer. J. Math. 100(1978), pp987-994.

Defintion2

• Escardo, Martín , Lawson, Jimmie and Simpson, Alex, Comparing Cartesian closed categories of (core) compactly generated spaces.[J] Topology Appl. 143, No. 1-3, 105-145 (2004).

• K.H. Hofmann, M. Mislove, Local compactness and continuous lattices, in: B. Banaschewski, R.-E. Hoffmann (Eds.), Continuous Lattices, in: Lecture Notes in Math., vol. 871, Springer, Berlin, 1981, pp. 209-248.