## 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.

### MSC:

 54C08 Weak and generalized continuity