A generalisation of the functional approach to compactness

A categorical approach to absolute closure

“…In the second part of the paper we show a relationship of these notions with some compactness notions. In particular, the interesting aspect that justifies our two parameter approach is the relationship with the notion of "asymmetric compactness" introduced in [18]. Some examples are provided.…”

“…A notion of "asymmetric compactness" was recently introduced by D. Holgate in [18]. It is a more general version than the classical notion of compactness with respect to a closure operator since it depends on two closure operators.…”

“…From [18], we know that KΣ-compact = countably compact. Thus, by Proposition 4.8, countably compact implies strongly (Σ, Top 2 )-closed.…”