On Multifunctions 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: This study introduces and examines upper and lower R−I−continuous multifunctions in ideal topological spaces. It also considers two weaker variants, namely upper and lower almost R−I−continuous multifunctions and upper and lower weakly R−I−continuous multifunctions.
Study Design: The investigation is theoretical.
Place and Duration of Study: The work was conducted in the Department of Mathematics, St. Joseph’s College (Autonomous), Devagiri, Calicut, India.
Methodology: Logical deduction was used to derive definitions, equivalence conditions, theorems, and related consequences from established concepts in topology and ideal topological spaces.
Results: Characterisations of upper and lower R−I−continuity were obtained in terms of inverse images, R−I−open and R−I−closed sets, neighbourhoods, closures, interiors, graph multifunctions, compactness, connectedness, and the R−I−kernel. The behaviour of compositions was examined in detail, and conditions connecting the continuity of a multifunction with that of its graph multifunction were established. The study also characterised the almost and weak forms of R−I−continuity and clarified the implication relations among the introduced classes.
Conclusion: The results provide a unified theoretical treatment of upper and lower R−I−continuous multifunctions and their almost and weak variants within a single ideal-topological framework. The established characterisations and implication relations may support further theoretical investigations of generalised continuity in ideal topological spaces.
Keywords: Ideal topological space, multifunction, upper R−I−continuity, lower R−I−continuity, almost R−I−continuity, weak R−I−continuity, graph multifunction, R−I−compactness, R−I−connectedness, R−I−kernel