Almost cl-supercontinuous functions
Keywords:Almost clopen map, Almost cl-supercontinuous function, (almost) z-supercontinuous function, Clopen almost closed graphs, Almost zero dimensional space, Hyperconnected space
Reilly and Vamanamurthy introduced the class of ‘clopen maps’ ( ‘cl-supercontinuous functions’). Subsequently generalizing clopen maps, Ekici defined and studied almost clopen maps( almost cl-supercontinuous functions). Continuing in the spirit of Ekici, here basic properties of almost clopen maps are studied. Behavior of separation axioms under almost clopen maps is elaborated. The interrelations between direct and inverse transfer of topological properties under almost clopen maps are investigated. The results obtained in the process generalize, improve and strengthen several known results in literature including those of Ekici, Singh, and others.
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