in this paper, a new definition of fuzzy bounded sets and totallyfuzzy bounded sets is introduced and properties of such sets are studied. thena relation between totally fuzzy bounded sets and n-compactness is discussed.finally, a geometric characterization for fuzzy totally bounded sets in i- topologicalvector spaces is derived.

according to a class of constrained‎ ‎minimization problems‎, ‎the schwartz symmetrization process and the‎ ‎compactness lemma of strauss‎, ‎we prove that there is a‎ ‎nontrivial ground state solution for a class of $p$-laplace‎ ‎equations without the ambrosetti-rabinowitz condition‎.

Compactness and closedness are some of the important properties for studying topological spaces. Several types of these concepts (semi-compactness, pre-compactness, β-compactness,. . ., S-closedness, H-closedness, etc) occur in the literature. In this paper, we applied concept of φ operation which defined by Csaszar [8] to unify and generalized several characterizations and properties of lots o...