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We define new classes of sets called δβI-open set, δα - I-open set, δβ - I-set, semi* - I-open set, sδI - g-closed set in ideal topological spaces. Using these sets, we obtain decompositions of continuity and complete continuity in ideal topological spaces. Also, we investigate some properties of these sets and relationship other generalized sets. [ABSTRACT FROM AUTHOR]

We introduce the notions of δ-t-sets, δβ- t-sets, δ- B-continuity and δβ - B-continuity and obtain decompositions of continuity and complete continuity. [ABSTRACT FROM AUTHOR]

We establish a general sharp inequality which holds for the family of conformally flat submanifolds in real space form. We show that this inequality does not hold for arbitrary submanifolds in real space forms. We also provide several applications of the inequality. [ABSTRACT FROM AUTHOR]

Przemski [5] introduced D(c,α)-set, D(c,p)-set, D(c,s)-set and D(α,p)-set to obtain several decompositions of continuity. In this paper, we extend these sets and obtain new decompositions of continuity via idealization. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new types of sets called (1,2)*-D(α,p) sets, (1,2)*-D(α,s) sets, (1,2)*-D(c,α) sets, (1,2)*-D(c,s) sets and (1,2)*-D(c,p) sets and new classes of mappings called (1,2)*-D(α,p) continuous, (1,2)*-D(α,s) continuous, (1,2)*-D(c,α) continuous, (1,2)*-D(c,s) continuous and (1,2)*-D(c,p) continuous mappings. We obtain several characterizations of these classes, study their bitopological properties, and investigate their relation with other bitopological sets and mappings. [ABSTRACT FROM AUTHOR]