Related papers: \alpha $ $^m $ Continuous Maps in Topological Spac…
In this paper, we derive more on $\alpha^{m}$-continuous functions and $\alpha^{m}$-irresolute functions with $\alpha^{m}$-open maps and $\alpha^{m}$-closed maps in topological spaces also we introduce $I_{\alpha^{m}}(A)$ and…
In this paper, we introduce the concept of $e^\star_{[\gamma,\gamma']}$-open sets in topological spaces and examine their properties in detail. Additionally, we propose a new class of functions, termed $(e^\star_{[\gamma,\gamma']},\…
We study the maps between topological spaces whose composition with Baire class $\alpha$ maps also belongs to the $\alpha$'th Baire class and give characterizations of such maps
In this paper, we introduce $T_{\alpha^{m}}$-Spaces, $\alpha^{m}$-closed maps and $\alpha^{m}$-open maps and studied some of their properties.
In this paper, we establish some new integral inequalities for $(\alpha, m)-$convex functions and quasi-convex functions, respectively. Our results in special cases recapture known results.
In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence, some versions of…
The aim of the current paper is to introduce a new class of contractive mappings, which are contracting (a feature of) triangles. We prove that maps contracting triangles are continuous and give the fixed point result for such mappings. We…
Our primary aim is to explore a sufficient condition for the class of meromorphically convex functions of order $\alpha$, where $0 \leq \alpha < 1$. The investigation will focus on studying a class of continuous functions defined on…
This paper introduces a novel topology, referred to as the star topology, on finite graphs. By treating vertices and edges as points in a unified space, we explore continuous maps between Bare representations of a graph and their…
In this paper, we obtain some new inequalities for ({\alpha},m)-convex functions. The analysis used in the proofs is fairly elementary and based on the use of Power-mean inequality.
We shall generalize the concept of $z=(1-t)x\oplus ty$ to $n$ times which contains to verifying some their properties and inequalities in CAT(0) spaces. In the sequel with introducing of $\alpha$-nonexpansive mappings, we obtain some fixed…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…
In this paper, we continue studying the properties of $\gamma$-semi-continuous and $\gamma$-semi-open functions introduced in [5].
Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections. This class contains continuous mappings as well as…
We introduce vectorial and topological continuities for functions defined on vector metric spaces and illustrate spaces of such functions. Also, we describe some fundamental classes of vector valued functions and extension theorems.
For a topological space $X$ we study continuous maps $f : X\to \mathbb R^m$ such that images of every pairwise distinct $k$ points are affinely (linearly) independent. Such maps are called affinely (linearly) $k$-regular embeddings. We…
A classic problem in analysis is to solve nonlinear equations of the form \begin{equation*} F(x)=0, \end{equation*} where $F:D^n\to \mathbb{R}^m$ is a continuous map of the closed unit disk $D^n\subset\mathbb{R}^n$ in $\mathbb{R}^m$. A…
We survey recent developments on mapping class groups of surfaces of infinite topological type.
The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…
Stable fold maps are fundamental tools in a generalization of the theory of Morse functions on smooth manifolds and its application to studies of geometric properties of smooth manifolds. Round fold maps were introduced as stable fold maps…