Closed classes of functions, generalized constraints, and clusters

Erkko Lehtonen

doi:10.1007/s00012-010-0071-6

Closed classes of functions, generalized constraints, and clusters

Erkko Lehtonen

Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Classes of functions of several variables on arbitrary nonempty domains that are closed under permutation of variables and addition of dummy variables are characterized by generalized constraints, and hereby Hellerstein's Galois theory of functions and generalized constraints is extended to infinite domains. Furthermore, classes of operations on arbitrary nonempty domains that are closed under permutation of variables, addition of dummy variables, and composition are characterized by clusters, and a Galois connection is established between operations and clusters.

Original language	British English
Pages (from-to)	203-234
Number of pages	32
Journal	Algebra Universalis
Volume	63
Issue number	2-3
DOIs	https://doi.org/10.1007/s00012-010-0071-6
State	Published - 2010

Keywords

closed set
cluster
function algebra
Galois connection
generalized constraint

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10.1007/s00012-010-0071-6

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title = "Closed classes of functions, generalized constraints, and clusters",

abstract = "Classes of functions of several variables on arbitrary nonempty domains that are closed under permutation of variables and addition of dummy variables are characterized by generalized constraints, and hereby Hellerstein's Galois theory of functions and generalized constraints is extended to infinite domains. Furthermore, classes of operations on arbitrary nonempty domains that are closed under permutation of variables, addition of dummy variables, and composition are characterized by clusters, and a Galois connection is established between operations and clusters.",

keywords = "closed set, cluster, function algebra, Galois connection, generalized constraint",

author = "Erkko Lehtonen",

note = "Funding Information: Presented by R. P{\"o}schel. Received July 29, 2008; accepted in final form September 2, 2009. 2000 Mathematics Subject Classification: Primary: 08A40; Secondary: 06A15. Key words and phrases: function algebra, closed set, generalized constraint, cluster, Galois connection. This research was supported by the Academy of Finland, grant #120307.",

year = "2010",

doi = "10.1007/s00012-010-0071-6",

language = "British English",

volume = "63",

pages = "203--234",

journal = "Algebra Universalis",

issn = "0002-5240",

publisher = "Birkhauser Verlag Basel",

number = "2-3",

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TY - JOUR

T1 - Closed classes of functions, generalized constraints, and clusters

AU - Lehtonen, Erkko

N1 - Funding Information: Presented by R. Pöschel. Received July 29, 2008; accepted in final form September 2, 2009. 2000 Mathematics Subject Classification: Primary: 08A40; Secondary: 06A15. Key words and phrases: function algebra, closed set, generalized constraint, cluster, Galois connection. This research was supported by the Academy of Finland, grant #120307.

PY - 2010

Y1 - 2010

N2 - Classes of functions of several variables on arbitrary nonempty domains that are closed under permutation of variables and addition of dummy variables are characterized by generalized constraints, and hereby Hellerstein's Galois theory of functions and generalized constraints is extended to infinite domains. Furthermore, classes of operations on arbitrary nonempty domains that are closed under permutation of variables, addition of dummy variables, and composition are characterized by clusters, and a Galois connection is established between operations and clusters.

AB - Classes of functions of several variables on arbitrary nonempty domains that are closed under permutation of variables and addition of dummy variables are characterized by generalized constraints, and hereby Hellerstein's Galois theory of functions and generalized constraints is extended to infinite domains. Furthermore, classes of operations on arbitrary nonempty domains that are closed under permutation of variables, addition of dummy variables, and composition are characterized by clusters, and a Galois connection is established between operations and clusters.

KW - closed set

KW - cluster

KW - function algebra

KW - Galois connection

KW - generalized constraint

UR - http://www.scopus.com/inward/record.url?scp=77958474222&partnerID=8YFLogxK

U2 - 10.1007/s00012-010-0071-6

DO - 10.1007/s00012-010-0071-6

M3 - Article

AN - SCOPUS:77958474222

SN - 0002-5240

VL - 63

SP - 203

EP - 234

JO - Algebra Universalis

JF - Algebra Universalis

IS - 2-3

ER -

Closed classes of functions, generalized constraints, and clusters

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