A bitopological view on cocompact extensions (Q1183639)

Let \(\tau_ 1\) and \(\tau_ 2\) be topologies on a set \(X\). The topology \(\tau_ 1\) is called a cotopology of \(\tau_ 2\) if \(\tau_ 1\subset\tau_ 2\) and \(\tau_ 2\) is regular with respect to \(\tau_ 1\). The space \((X,\tau_ 1)\) is called a cospace of the space \((X,\tau_ 2)\). The space \((X,\tau_ 2)\) is said to be cocompact if there exists a compact cotopology \(\tau_ 1\) and \(\tau_ 2\). The authors discuss cotopology, cocompactness and related topics in terms of bitopological theory.