Some results related to new type of continuity, compactness, and connectedness in topological spaces

Several properties of F-continuous functions, F-compact spaces, and F-connected spaces in the setting of topological spaces were investigated in this paper. The relationships among these concepts and their classical counterparts were established, and their preservation properties under mappings were studied. Characterizations of F-compactness using the finite intersection property were obtained, and several equivalent conditions for F-connected spaces were presented. Furthermore, The behavior of F-connectedness under surjective F-continuous mappings and F-homeomorphisms were examined. The results extend classical topological notions within the framework of F-open sets and provide a foundation for further research in generalized topology.