Abstract
AbstractIn the present paper, we have defined a wide class of sets by using thetopology of the space X, which we call a class of fine-open sets. This newcollection contains open sets, -open sets, -open sets, pre-open sets andsemi-open sets. In view of this class of fine-open sets, we have defined afine-irresolute mapping which may be used in some branches of quantumphysics where the homeomorphic images of the given sets are required withhigh accuracy. Using our idea of fine-open sets, we have also defined aclass of various continuous functions like fine-continuous, f-continuous, fcontinuous,sf-continuous, pf-continuous, ff-continuous, ff-continuous,fsf-continuous, fpf-continuous, sf-irresolute, pf-irresolute and studied theirproperties. Our new class contains several continuous functions which are alreadydefined (cf. [Maheshwari S. N. and Thakur S. S., On -irresolute mappings,Tamkang J. Math ., 11(1980), 209 ? 214], [Beceren Y. and Noiri T.,Strongly precontinuous functions. Acta. Math., Hunger, 108(1 ? 2)(2005),147 ? 53]).
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