Hereditary properties in isotonic spaces

Abstract EN

An isotonic space (X; cl) is a set X with isotonic operator cl : P(X)→ P(X) which sates es cl(∅) = ∅ and cl(A) ⊆ cl (B) whenever A ⊆ B ⊆ X.

Many properties which hold in topological spaces hold in isotonic spaces as well.

We explore the topological concepts of lower separation axioms, higher separation axioms and connectedness for isotonic spaces, and we establish that some of these concepts are hereditary properties in isotonic spaces and some are not.