On pre-\(\theta\)-open sets and two classes of functions. (English) Zbl 1152.54302
Summary: We introduce the notions of pro-\(\theta\)-derived, pre-\(\theta\)-border, pre-\(\theta\)-frontier and pre-\(\theta\)-exterior of a set and study some of their basic properties. We also introduce two classes of functions called \(\theta\)-preopen functions and \(\theta\)-precloscd functions. We obtain their characterizations, their basic properties and their relationships with other types of functions between topological spaces.
MSC:
54A05 | Topological spaces and generalizations (closure spaces, etc.) |
54C10 | Special maps on topological spaces (open, closed, perfect, etc.) |
54D10 | Lower separation axioms (\(T_0\)–\(T_3\), etc.) |
54C08 | Weak and generalized continuity |