Continuity

Guerino Mazzola; Maria Mannone; Yan Pang

doi:10.1007/978-3-319-42937-3_30

Continuity

Guerino Mazzola
, Maria Mannone
, Yan Pang

Music (Twin Cities)

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

Despite the rich algebraic formalism of monoids, groups, rings, and modules, we lack a type of analysis that does not compare objects by their transformational relations, such as symmetries or module homomorphisms, but by their similarity—referring to the paradigm of deformation. This type of relationship is what topology, the mathematics of continuity, is about.

Original language	English (US)
Title of host publication	Computational Music Science
Publisher	Springer Nature
Pages	257-262
Number of pages	6
DOIs	https://doi.org/10.1007/978-3-319-42937-3_30
State	Published - 2016

Publication series

Name	Computational Music Science
ISSN (Print)	1868-0305
ISSN (Electronic)	1868-0313

Bibliographical note

Publisher Copyright:
© 2016, Springer International Publishing Switzerland.

Keywords

Module Homomorphism
Open Interval
Open Neighborhood
Topological Space
Transformational Relation

Publisher link

10.1007/978-3-319-42937-3_30

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title = "Continuity",

abstract = "Despite the rich algebraic formalism of monoids, groups, rings, and modules, we lack a type of analysis that does not compare objects by their transformational relations, such as symmetries or module homomorphisms, but by their similarity—referring to the paradigm of deformation. This type of relationship is what topology, the mathematics of continuity, is about.",

keywords = "Module Homomorphism, Open Interval, Open Neighborhood, Topological Space, Transformational Relation",

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AU - Mazzola, Guerino

AU - Mannone, Maria

AU - Pang, Yan

PY - 2016

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AB - Despite the rich algebraic formalism of monoids, groups, rings, and modules, we lack a type of analysis that does not compare objects by their transformational relations, such as symmetries or module homomorphisms, but by their similarity—referring to the paradigm of deformation. This type of relationship is what topology, the mathematics of continuity, is about.

KW - Module Homomorphism

KW - Open Interval

KW - Open Neighborhood

KW - Topological Space

KW - Transformational Relation

UR - https://www.scopus.com/pages/publications/85136699071

UR - https://www.scopus.com/pages/publications/85136699071#tab=citedBy

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DO - 10.1007/978-3-319-42937-3_30

M3 - Chapter

AN - SCOPUS:85136699071

T3 - Computational Music Science

SP - 257

EP - 262

BT - Computational Music Science

PB - Springer Nature

ER -

Continuity

Abstract

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