In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ with respect to the pseudo-monotonicity its Clarke-Rockafellar Sub-differential. We extend results characterizations non-smooth monotonicity sub-differentials spaces.

In this paper, we introduce two different notions of generalized supra soft sets namely supra A--soft sets and supra soft locally closed sets in supra soft topological spaces, which are weak forms of supra open soft sets and discuss their relationships with each other and other supra open soft sets [{it International Journal of Mathematical Trends and Technology} (IJMTT), (2014) Vol. 9 (1):37--...

The aim of this paper is to introduce various functions associated with semi*α-open sets. Here semi*αcontinuous, semi*α-irresolute, contra-semi*α-continuous and contra-semi*α-irresolute functions are defined. Characterizations for these functions are given. Further their fundamental properties are investigated. Many other functions associated with semi*α-open sets and their contra versions are ...

In [6], a sufficient condition for space to be ?-stratifiable was presented and it asked whether the is necessary. Jin et al [4] gave negative answer question by showing that with zero-dimensional. this paper, we show precisely an almost discrete space. Moreover, introduce notions of strongly lower (upper) semi-continuous functions, which characterizations spaces are presented.