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Connectivity Preserving Multivalued Functions in Digital Topology
[article]

2015
*
arXiv
*
pre-print

We study connectivity preserving

arXiv:1504.02174v2
fatcat:fpdxxjyg4jbzrhhuyxa2jgz73m
*multivalued**functions*between digital images. This notion generalizes that*of*continuous*multivalued**functions*studied mostly in the setting*of*the digital plane Z^2. ... We show that connectivity preserving*multivalued**functions*, like continuous*multivalued**functions*, are appropriate models for digital morpholological operations. ...*Composition*Connectivity preservation*of**multivalued**functions*is preserved by*compositions*. ...##
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An ordered framework for partial multivalued functors
[article]

2015
*
arXiv
*
pre-print

The category Rel

arXiv:1511.00746v1
fatcat:3odk4wjhpfef3oxjbvqytqdv3m
*of*sets and relations intimately ties the notions*of**function*, partial*multivalued**function*, and direct image under a*function*through the description*of*Rel as the Kleisli category*of*... We present a suitable framework to obtain a similar relationship between the concepts*of*functor, partial*multivalued*functor, and the direct image under a functor. ... Extending the notion*of*a partial*multivalued**function*to categories, we define a partial*multivalued*functor F : C + → D between two small categories to consist*of*a partial*multivalued**function*F : obC ...##
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Multivalued Functions in Digital Topology
[article]

2017
*
arXiv
*
pre-print

We study several types

arXiv:1703.01700v1
fatcat:kgkg4mrgujawdoo6e3slasjyyq
*of**multivalued**functions*in digital topology. ... In section 4, we studied properties*of**multivalued**functions*that are preserved by*composition*. In section 5, we studied retractions and extensions*of*structured*multivalued**functions*. ... In section 3, we studied relations between continuous*multivalued**functions*and other structured types*of**multivalued**functions*. ...##
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Thinning Algorithms as Multivalued ${\mathcal{N}}$ -Retractions
[chapter]

2009
*
Lecture Notes in Computer Science
*

*functions*. ... particular kind

*of*

*multivalued*retraction, with the property that each point is retracted to its neighbors. ... Since the

*composition*

*of*k-continuous

*multivalued*

*functions*is a k-continuous

*multivalued*

*function*, we have the following result. Corollary 1. ...

##
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Approximate Fixed Point Properties in Digital Topology
[article]

2020
*
arXiv
*
pre-print

We study the approximate fixed point property (AFPP) for continuous single-valued

arXiv:1911.07400v3
fatcat:cxox5y2b5bfihj4i6vd5untgqu
*functions*and for continuous*multivalued**functions*in digital topology. ... Digitally continuous*multivalued**functions*A*multivalued**function*f from X to Y assigns a subset*of*Y to each point*of*x. We will write f : X ⊸ Y . ... It is known [10] that a*composition**of*digitally continuous*multivalued**functions*need not be continuous. However, we have the following. Theorem 2.7. [10] Let X ⊂ Z v , Y ⊂ Z n , Z ⊂ Z p . ...##
###
Page 251 of Automation and Remote Control Vol. 53, Issue 2
[page]

1992
*
Automation and Remote Control
*

In [10] there is a brief description

*of*a*composition*algebra*of*polynomials as a computer model for representation*of**functions*in*multivalued*logic by means*of*arithmetic operations. ... Further development in computer technology and mathematical software also requires discovery*of*new and nontraditional approaches to realization*of**functions*(or systems*of**functions*) in*multivalued*logic ...##
###
Multidimensional topological Galois theory
[article]

2019
*
arXiv
*
pre-print

The theory studies topological obstruction to solvability

arXiv:1904.07228v1
fatcat:6yqt5msjwfez5owjcgjbssmlf4
*of*equations "in finite terms" (i.e. to their solvability by radicals, by elementary*functions*, by quadratures and so on). ... In this preprint we present an outline*of*the multidimensional version*of*topological Galois theory. ... For*functions**of*one variable, we use a different, extended definition*of*operations on*multivalued**functions*, in which the*multivalued**function*is viewed as a single object. ...##
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On the roots of the substitution Dickson polynomials

2002
*
International Journal of Mathematics and Mathematical Sciences
*

We show that under the

doi:10.1155/s0161171202007561
fatcat:uj3nsoyk5ze6llutxjfgl7iohy
*composition**of**multivalued**functions*, the set*of*the y-radical roots*of*the Dickson substitution polynomial g d (x, a)−g d (y, a) is generated by one*of*the roots. ... Hence, we show an expected generalization*of*the fact that, under the*composition**of*the*functions*, the y-radical roots*of*x d − y d are generated by ζ d y. ... ,σ m1 (y) generate the set*of*roots {σ jk (y) : 1 ≤ j ≤ m, 1 ≤ k ≤ n}. radical expressions in y over the algebraic closure*of*the field*of**functions*F q (y); (ii) under the*composition**of**multivalued**functions*...##
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An intrinsic description of shape

1992
*
Transactions of the American Mathematical Society
*

We give in this paper a description

doi:10.1090/s0002-9947-1992-1028311-x
fatcat:oasgaox7qfhhhkfrnjvigwzcu4
*of*the shape category*of*compacta in terms*of**multivalued*maps. ... We present many applications*of*this new formulation*of*shape. ... By a*multivalued**function*F : X -> Y we mean a*function*assigning to each point x £ X a nonempty closed subset F(x)*of*Y . ...##
###
Page 1 of Journal of the Atmospheric Sciences Vol. 64, Issue 1
[page]

2007
*
Journal of the Atmospheric Sciences
*

To see the dependence

*of*the*multivalued**functional*lines*of*gp versus Wp on the initial value (intensity and structure)*of*the NAO’ event, we can consider B(x, 0) = B, cos(ex) and B(x, 0) = Bo sech(\/ ... Thus, it is natural to conclude that the NAO free mode because the*multivalued**functional*relation- ship*of*the scatter diagram is a manifestation*of*strongly nonlinear isolated structures. ...##
###
An Intrinsic Description of Shape

1992
*
Transactions of the American Mathematical Society
*

We give in this paper a description

doi:10.2307/2153955
fatcat:q3jp3k72bjaeflxrdek2q4nt5e
*of*the shape category*of*compacta in terms*of**multivalued*maps. ... We present many applications*of*this new formulation*of*shape. ... By a*multivalued**function*F : X -> Y we mean a*function*assigning to each point x £ X a nonempty closed subset F(x)*of*Y . ...##
###
Galois Connections for Generalized Functions and Relational Constraints
[article]

2015
*
arXiv
*
pre-print

These mappings are called

arXiv:1508.01567v1
fatcat:nmozetzzj5estj4hkmiqrghyte
*multivalued**functions*, and they generalize total and partial*functions*. ... In this paper we focus on*functions**of*the form A^n→P(B), for possibly different arbitrary non-empty sets A and B, and where P(B) denotes the set*of*all subsets*of*B. ... By a class*of**multivalued**functions*we simply mean a set*of**multivalued**functions**of*various arities. ...##
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Page 8187 of Mathematical Reviews Vol. , Issue 99m
[page]

1999
*
Mathematical Reviews
*

From the summary: “We introduce

*composition*, Cartesian and direct products*of*fuzzy*multivalued*mappings and study their properties. ... Special attention is paid to the expressions for the images under the products*of*fuzzy*multivalued*mappings. For*composition*the properties*of*the images in terms*of*cuts are also studied. ...##
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Digitally Continuous Multivalued Functions, Morphological Operations and Thinning Algorithms

2011
*
Journal of Mathematical Imaging and Vision
*

Our approach, which uses

doi:10.1007/s10851-011-0277-z
fatcat:ovs2unbb2zbclnbbdpog7acnke
*multivalued**functions*, provides a better framework to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous ...*functions*. ... Acknowledgements The authors thank the referees for helpful comments and suggestions which have helped to improve the final version*of*the paper. ...##
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One dimensional topological Galois theory
[article]

2019
*
arXiv
*
pre-print

The theory studies topological obstruction to solvability

arXiv:1904.03341v1
fatcat:57zjc67anjfudhhzq5kmwgx7ii
*of*equations "in finite terms" (i.e. to their solvabilty by radicals, by elementary*functions*, by quadratures and so on). ... In the preprint we present an outline*of*the one dimensional version*of*topological Galois theory. ... If a*multivalued**function*f can be obtained from single valued S-*functions*by integration, differentiation, meromorphic operations,*compositions*, solutions*of*algebraic equations and linear differential ...
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