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Quasicontinuous spaces

Jing Lu, Bin Zhao, Kaiyun Wang, Dong Sheng Zhao (2022)

Commentationes Mathematicae Universitatis Carolinae

We lift the notion of quasicontinuous posets to the topology context, called quasicontinuous spaces, and further study such spaces. The main results are: (1) A T 0 space ( X , τ ) is a quasicontinuous space if and only if S I ( X ) is locally hypercompact if and only if ( τ S I , ) is a hypercontinuous lattice; (2) a T 0 space X is an S I -continuous space if and only if X is a meet continuous and quasicontinuous space; (3) if a C -space X is a well-filtered poset under its specialization order, then X is a quasicontinuous space...

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