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Connectivity Preserving Multivalued Functions in Digital Topology [article]

Laurence Boxer, P. Christopher Staecker
2015 arXiv   pre-print
We study connectivity preserving 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.  ... 
arXiv:1504.02174v2 fatcat:fpdxxjyg4jbzrhhuyxa2jgz73m

An ordered framework for partial multivalued functors [article]

Alveen Chand, Ittay Weiss
2015 arXiv   pre-print
The category Rel 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  ... 
arXiv:1511.00746v1 fatcat:3odk4wjhpfef3oxjbvqytqdv3m

Multivalued Functions in Digital Topology [article]

Laurence Boxer
2017 arXiv   pre-print
We study several types 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.  ... 
arXiv:1703.01700v1 fatcat:kgkg4mrgujawdoo6e3slasjyyq

Thinning Algorithms as Multivalued ${\mathcal{N}}$ -Retractions [chapter]

Carmen Escribano, Antonio Giraldo, María Asunción Sastre
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.  ... 
doi:10.1007/978-3-642-04397-0_24 fatcat:xht62jrvgvehtpbexegl5msrmy

Approximate Fixed Point Properties in Digital Topology [article]

Laurence Boxer
2020 arXiv   pre-print
We study the approximate fixed point property (AFPP) for continuous single-valued 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 .  ... 
arXiv:1911.07400v3 fatcat:cxox5y2b5bfihj4i6vd5untgqu

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]

Askold Khovanskii
2019 arXiv   pre-print
The theory studies topological obstruction to solvability 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.  ... 
arXiv:1904.07228v1 fatcat:6yqt5msjwfez5owjcgjbssmlf4

On the roots of the substitution Dickson polynomials

Javier Gomez-Calderon
2002 International Journal of Mathematics and Mathematical Sciences  
We show that under the 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  ... 
doi:10.1155/s0161171202007561 fatcat:uj3nsoyk5ze6llutxjfgl7iohy

An intrinsic description of shape

José M. R. Sanjurjo
1992 Transactions of the American Mathematical Society  
We give in this paper a description 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 .  ... 
doi:10.1090/s0002-9947-1992-1028311-x fatcat:oasgaox7qfhhhkfrnjvigwzcu4

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

Jose M. R. Sanjurjo
1992 Transactions of the American Mathematical Society  
We give in this paper a description 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 .  ... 
doi:10.2307/2153955 fatcat:q3jp3k72bjaeflxrdek2q4nt5e

Galois Connections for Generalized Functions and Relational Constraints [article]

Miguel Couceiro
2015 arXiv   pre-print
These mappings are called 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.  ... 
arXiv:1508.01567v1 fatcat:nmozetzzj5estj4hkmiqrghyte

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.  ... 

Digitally Continuous Multivalued Functions, Morphological Operations and Thinning Algorithms

Carmen Escribano, Antonio Giraldo, María Asunción Sastre
2011 Journal of Mathematical Imaging and Vision  
Our approach, which uses 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.  ... 
doi:10.1007/s10851-011-0277-z fatcat:ovs2unbb2zbclnbbdpog7acnke

One dimensional topological Galois theory [article]

Askold Khovanskii
2019 arXiv   pre-print
The theory studies topological obstruction to solvability 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  ... 
arXiv:1904.03341v1 fatcat:57zjc67anjfudhhzq5kmwgx7ii
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