منابع مشابه
Categorically-algebraic topology and its applications
This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...
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This manuscript will be published as Chapter 5 in Wiley’s textbook Mathematical Tools for Physicists, 2nd edition, edited by Michael Grinfeld from the University of Strathclyde. The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebr...
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Algebraic topology is at a point of inflection today, and the Spring 2014 Algebraic Topology program at MSRI reflects the excitement of this moment. The introductory workshop, with more than 200 participants, provided careful introductions to the dominant themes leading up to this moment, giving an informative welcome to the many young researchers in the program and attending the conference. Th...
متن کاملcategorically-algebraic topology and its applications
this paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. it incorporates the most important settings of lattice-valued topology, including poslat topology of s.~e.~rodabaugh, $(l,m)$-fuzzy topology of t.~kubiak and a.~v{s}ostak, and $m$-fuzzy topology on $l$-fuzzy sets of c.~guido. moreover, its respe...
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In this paper, we present a new version of cochains in Algebraic Topology, starting with “quantum differential forms”. This version provides many examples of modules over the braid group, together with a control of the non commutativity of cup-products on the cochain level. If the quantum parameter q is equal to 1, we essentially recover the commutative differential graded algebra of de Rham-Su...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1981
ISSN: 0019-2082
DOI: 10.1215/ijm/1256047364