On the definitions of some generalized forms of continuity under minimal conditions. (English) Zbl 0972.54011

The authors define a minimal structure on a set \(X\) to be a family \(m_X\) of subsets of \(X\) containing the empty set and \(X\) itself. In a natural way, one can define the closure and the interior of a subset of \(X\) with respect to a given minimal structure \(m_X\), as well as the notion of \(m\)-continuity between a set with minimal structure and a topological space. The authors study \(m\)-continuous functions as well as concepts such as \(m\)-\(T_2\) spaces, \(m_X\)-compactness and \(m_X\)-connectedness.


54C08 Weak and generalized continuity