γ-sets andγ-continuous functions

Γ-sets and Γ-continuous Functions

Micro Tangent Sets of Continuous Functions

Motivated by the concept of tangent measures and by H. Fürstenberg’s definition of microsets of a compact set A we introduce micro tangent sets and central micro tangent sets of continuous functions. It turns out that the typical continuous function has a rich (universal) micro tangent set structure at many points. The Brownian motion, on the other hand, with probability one does not have graph...

K -Trivial Closed Sets and Continuous Functions

We investigate the notion of K-triviality for closed sets and continuous functions. Every K-trivial closed set contains a K-trivial real. There exists a K-trivial Π 1 class with no computable elements. For any K-trivial degree d, there is a K-trivial continuous function of degree d.

N . Rajesh and V . Vijayabharathi ON ALMOST ( γ , γ ′ ) - ( β , β ′ ) - s - CONTINUOUS FUNCTIONS

The aim of this paper is to introduce and study a new class of functions called almost (γ, γ′)-(β, β′)-s-continuous functions in topological spaces by using (γ, γ′)-semiopen sets.

On Some Properties of Sets Blocking Almost Continuous Functions

We define operators E( · ) and N ( · ) for blocking sets for almost continuous functions. Using language of these operators we give new proofs for some classical theorems and prove some new theorems. Finally, we make some remarks regarding uniform limits of almost continuous functions.