On inductively open real functions

On Inductively Open Real Functions

In this note, given a locally connected topological space X, we characterize those continuous and locally nonconstant real functions on X which are inductively open there. Throughout this note, X denotes a locally connected topological space. Let / be a real function on X. We recall that / is said to be inductively open in X (see [1]) if there exists a set X* Q X such that f{X*) = f(X) and the ...

Effectively Open Real Functions

A function f is continuous iff the pre-image f[V ] of any open set V is open again. Dual to this topological property, f is called open iff the image f [U ] of any open set U is open again. Several classical Open Mapping Theorems in Analysis provide a variety of sufficient conditions for openness. By the Main Theorem of Recursive Analysis, computable real functions are necessarily continuous. I...

On weakly eR-open functions

The main goal of this paper is to introduce and study a new class of function via the notions of $e$-$theta$-open sets and $e$-$theta$-closure operator which are defined by Özkoç and Aslım [10] called weakly $eR$-open functions and $e$-$theta$-open functions. Moreover, we investigate not only some of their basic properties but also their relationships with other types of already existing topolo...

on weakly er-open functions

the main goal of this paper is to introduce and study a new class of function via the notions of $e$-$theta$-open sets and $e$-$theta$-closure operator which are defined by özkoç and aslım cite{10} called weakly $er$-open functions and $e$-$theta$-open functions. moreover, we investigate not only some of their basic properties but also their relationships with other types of already existing to...

On Pre-θ-Open Sets and Two Classes of Functions