On Contra-continuous Functions in Ideal Topological Space
M. V. Sangeetha *
Department of Mathematics, St. Joseph’s College (Autonomous) Devagiri, Calicut-673008, India.
*Author to whom correspondence should be addressed.
Abstract
Aims/Objectives: This study introduces and examines contra R − I− continuous functions and almost contra R − I− continuous functions in ideal topological spaces. It also investigates contra R − I−closed graphs and strongly contra R − I−closed graphs associated with these classes of mappings.
Study Design: Theoretical study in general topology.
Place and Duration of Study: Department of Mathematics, St. Joseph’s College (Autonomous), Devagiri, Calicut-673008, India.
Methodology: Deductive reasoning was applied to established concepts of ideal topological spaces, R − I−open and R − I−closed sets, local functions, kernels, separation axioms, and generalised continuity. Definitions were formulated, equivalent conditions were proved, and consequences were derived under specified topological assumptions.
Results: Equivalent characterisations of contra R − I−continuity were obtained through inverse images of open and closed sets, R − I−open neighbourhoods, kernels, and R − I−closures. Relationships with R − I−continuity, almost weakly R − I−continuity, connectedness, composition of mappings, and separation properties were established. Almost contra R−I−continuous functions were characterised using regular open and regular closed sets, and preservation results involving compactness-type properties were derived. Conditions ensuring contra R − I−closed and strongly contra R − I−closed graphs were also presented.
Conclusion: The study provides a unified theoretical treatment of contra-type continuity based on R − I−open sets. The results clarify, within a consistent formal framework, how these mappings interact with ideal-topological connectedness, separation axioms, compactness-related properties, and graph structures.
Keywords: Ideal topological space, contra-continuity, R−I−open set, R−I−closed set, contra R−I−continuous function, almost contra R−I−continuous function, R−I−connectedness, separation axioms, contra R − I−closed graph, strongly contra R − I−closed graph