Nearly continuous functions in digital images

1995 ◽  
Author(s):  
Longin J. Latecki ◽  
Frank Prokop
Keyword(s):  
Digital Images ◽  
Continuous Functions ◽  
Nearly Continuous

Almost Somewhat Near Continuity and Near Regularity

2021 ◽  
Vol 7 (1) ◽  
pp. 88-99
Author(s):  
Zanyar A. Ameen
Keyword(s):  
Continuous Function ◽  
Continuous Functions ◽  
One To One ◽  
Nearly Continuous

AbstractThe notions of almost somewhat near continuity of functions and near regularity of spaces are introduced. Some properties of almost somewhat nearly continuous functions and their connections are studied. At the end, it is shown that a one-to-one almost somewhat nearly continuous function f from a space X onto a space Y is somewhat nearly continuous if and only if the range of f is nearly regular.

scholarly journals Digital fixed points, approximate fixed points, and universal functions

2016 ◽  
Vol 17 (2) ◽  
pp. 159 ◽  
Author(s):  
Laurence Boxer ◽  
Ozgur Ege ◽  
Ismet Karaca ◽  
Jonathan Lopez ◽  
Joel Louwsma
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Digital Images ◽  
Continuous Functions ◽  
Universal Functions ◽  
Approximate Fixed Point ◽  
Fixed Point Properties ◽  
Digitally Continuous ◽  
Approximate Fixed Point Property ◽  
The Relationship

A. Rosenfeld [23] introduced the notion of a digitally continuous function between digital images, and showed that although digital images need not have fixed point properties analogous to those of the Euclidean spaces modeled by the images, there often are approximate fixed point properties of such images. In the current paper, we obtain additional results concerning fixed points and approximate fixed points of digitally continuous functions. Among these are several results concerning the relationship between universal functions and the approximate fixed point property (AFPP).

scholarly journals Coalgebras on Digital Images

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2082
Author(s):  
Sunyoung Lee ◽  
Dae-Woong Lee
Keyword(s):  
Commutative Ring ◽  
Digital Images ◽  
Continuous Functions ◽  
Contravariant Functor ◽  
Fundamental Properties

In this article, we investigate the fundamental properties of coalgebras with coalgebra comultiplications, counits, and coalgebra homomorphisms of coalgebras over a commutative ring R with identity 1R based on digital images with adjacency relations. We also investigate a contravariant functor from the category of digital images and digital continuous functions to the category of coalgebras and coalgebra homomorphisms based on digital images via the category of unitary R-modules and R-module homomorphisms.

scholarly journals Digital homotopy relations and digital homology theories

2021 ◽  
Vol 22 (2) ◽  
pp. 223
Author(s):  
P. Christopher Staecker
Keyword(s):  
Digital Images ◽  
Continuous Functions ◽  
Homology Theory ◽  
Simplicial Homology ◽  
Digitally Continuous ◽  
New Type ◽  
The Difference ◽  
Cubical Homology

In this paper we prove results relating to two homotopy relations and four homology theories developed in the topology of digital images.<br /><br />We introduce a new type of homotopy relation for digitally continuous functions which we call ``strong homotopy.'' Both digital homotopy and strong homotopy are natural digitizations of classical topological homotopy: the difference between them is analogous to the difference between digital 4-adjacency and 8-adjacency in the plane.<br /><br />We also consider four different digital homology theories: a simplicial homology theory by Arslan et al which is the homology of the clique complex, a singular simplicial homology theory by D. W. Lee, a cubical homology theory by Jamil and Ali, and a new kind of cubical homology for digital images with $c_1$-adjacency which is easily computed, and generalizes a construction by Karaca \&amp; Ege. We show that the two simplicial homology theories are isomorphic to each other, but distinct from the two cubical theories.<br /><br />We also show that homotopic maps have the same induced homomorphisms in the cubical homology theory, and strong homotopic maps additionally have the same induced homomorphisms in the simplicial theory.

scholarly journals On almost nearly continuous functions with reference to multifunctions

2009 ◽  
Vol 42 (1) ◽  
pp. 61-72
Author(s):  
Andrzej Rychlewicz
Keyword(s):  
Continuous Functions ◽  
Nearly Continuous

Abstract We deal with a new kind of continuity of multifunctions, namely almost nearly quasi-continuous multifunctions have been introduced. Several properties of almost nearly quasi-continuous and almost upper (lower) nearly quasicontinuous multifunctions have been obtained.

scholarly journals Semi-proximity continuous functions in digital images

1995 ◽  
Vol 16 (11) ◽  
pp. 1175-1187 ◽  
Author(s):  
Longin Latecki ◽  
Frank Prokop
Keyword(s):  
Digital Images ◽  
Continuous Functions

scholarly journals On the Digital Cohomology Modules

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1451 ◽  
Author(s):  
Dae-Woong Lee
Keyword(s):  
Commutative Ring ◽  
Digital Image ◽  
Finite Subset ◽  
Digital Images ◽  
Continuous Functions ◽  
Contravariant Functor ◽  
Adjacency Relation ◽  
The Relationship ◽  
Cohomology Modules

In this paper, we consider the digital cohomology modules of a digital image consisting of a bounded and finite subset of Zn and an adjacency relation. We construct a contravariant functor from the category of digital images and digital continuous functions to the category of unitary R-modules and R-module homomorphisms via the category of cochain complexes of R-modules and cochain maps, where R is a commutative ring with identity 1R. We also examine the digital primitive cohomology classes based on digital images and find the relationship between R-module homomorphisms of digital cohomology modules induced by the digital convolutions and digital continuous functions.

scholarly journals Locally closed sets andLC-continuous functions

1989 ◽  
Vol 12 (3) ◽  
pp. 417-424 ◽  
Author(s):  
M. Ganster ◽  
I. L. Reilly
Keyword(s):  
Topological Space ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Closed Set ◽  
Closed Sets ◽  
Generalized Continuity ◽  
Locally Closed Sets ◽  
Nearly Continuous

In this paper we introduce and study three different notions of generalized continuity, namely LC-irresoluteness, LC-continuity and sub-LC-continuity. All three notions are defined by using the concept of a locally closed set. A subset S of a topological space X is locally closed if it is the intersection of an open and a closed set. We discuss some properties of these functions and show that a function between topological spaces is continuous if and only if it is sub-LC-continuous and nearly continuous in the sense of Ptak. Several examples are provided to illustrate the behavior of these new classes of functions.

Sign in / Sign up

Export Citation Format

Share Document