K -Trivial Closed Sets and Continuous Functions

K-Triviality of Closed Sets and Continuous Functions

We investigate the notion of K-triviality for closed sets and continuous functions in 2N. For every K-trivial degreee d, there exists a closed set of degree d and a continuous function of degree d. Every K-trivial closed set contains a K-trivial real. There exists a K-trivial Π1 class with no computable elements. A closed set is K-trivial if and only if it is the set of zeroes of some K-trivial...

Decomposition of supra soft locally closed sets and supra SLC-continuity

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--...

Contra $beta^{*}$-continuous and almost contra $beta^{*}$-continuous functions

The notion of contra continuous functions was introduced and investigated by Dontchev. In this paper, we apply the notion of $beta^{*}$-closed sets in topological space to present and study a new class of functions called contra $beta^{*}$-continuous and almost contra $beta^{*}$-continuous functions as a new generalization of contra continuity.

Functionally closed sets and functionally convex sets in real Banach spaces

‎Let $X$ be a real normed  space, then  $C(subseteq X)$  is  functionally  convex  (briefly, $F$-convex), if  $T(C)subseteq Bbb R $ is  convex for all bounded linear transformations $Tin B(X,R)$; and $K(subseteq X)$  is  functionally   closed (briefly, $F$-closed), if  $T(K)subseteq Bbb R $ is  closed  for all bounded linear transformations $Tin B(X,R)$. We improve the    Krein-Milman theorem  ...

Semi-θ-Open Sets and New Classes of Maps