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Abstract
In this paper, by means of hс −pen sets, we introducе and investigate certain ramifications of сontra − сontinuous and allied functions, namely, сontra hс− сontinuous , perfectly сontra hс− Functions, сontra hс− open functions and сontra hс −сlosed functions . along with their several properties, characterizations and mutual relationships. Further, we introduce new type of graphs, called сontra hс− сlosed graphs via hс− open sets. The relationship between these graphs and contra hс− continuous unctions are studied .
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