Finite-to-one restrictions of continuous functions

Generalized Rings of Measurable and Continuous Functions

This paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

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.

On images of continuous functions from a compact manifold to Euclidean space

Restrictions of Smooth Functions to a Closed Subset

We first provide an approach to the recent conjecture of Bierstone-Milman-Paw lucki on Whitney’s old problem on C extendability of functions defined on a closed subset of a Euclidean space, using the higher order paratangent bundle they introduced. For example, the conjecture is affirmative for classical fractal sets. Next, we give a sharpened form of Spallek’s theorem on controllability of fla...

Pointfree topology version of image of real-valued continuous functions

Let $ { mathcal{R}} L$ be the ring of real-valued continuous functions on a frame $L$ as the pointfree  version of $C(X)$, the ring of all real-valued continuous functions on a topological space $X$. Since $C_c(X)$ is the largest subring of $C(X)$ whose elements have countable image, this motivates us to present the pointfree  version of $C_c(X).$The main aim of this paper is to present t...