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Mat. Sb., 2008, Volume 199, Number 2, Pages 3–26 (Mi msb1504)  

This article is cited in 12 scientific papers (total in 12 papers)

Capacity functor in the category of compacta

M. M. Zarichnyiab, O. R. Nykyforchync

a Ivan Franko National University of L'viv
b Rzeszów University
c Vasyl Stefanyk Precarpathian National University

Abstract: Spaces of upper-semicontinuous capacities on compacta are studied. It is proved that the capacity functor defines a monad in the category of compacta containing the monad of inclusion hyperspaces as a submonad. In addition, a metrization of the space of capacities of a compact metric space is defined. It is also proved that the capacity functor is open.
Bibliography: 17 titles.
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DOI: https://doi.org/10.4213/sm1504

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English version:
Sbornik: Mathematics, 2008, 199:2, 159–184

Bibliographic databases:

UDC: 515.122.5+517.518.11
MSC: Primary 54B30; Secondary 18B30, 54D30
Received: 23.01.2006 and 21.08.2007

Citation: M. M. Zarichnyi, O. R. Nykyforchyn, “Capacity functor in the category of compacta”, Mat. Sb., 199:2 (2008), 3–26; Sb. Math., 199:2 (2008), 159–184

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Hlushak I.D., Nykyforchyn O.R., “Submonads of the capacity monad”, Carpathian J. Math., 24:1 (2008), 56–67  mathscinet  zmath  isi
    2. Radul T., “A functional representation of capacity monad”, Topology, 48:2-4 (2009), 100–104  crossref  mathscinet  zmath  isi  scopus
    3. Nykyforchyn O.R., “The Sugeno integral and functional representation of the monad of lattice-valued capacities”, Topology, 48:2-4 (2009), 137–148  crossref  mathscinet  zmath  isi  scopus
    4. Nykyforchyn O., Repovš D., “Inclusion hyperspaces and capacities on Tychonoff spaces: functors and monads”, Topology Appl., 157:15 (2010), 2421–2434  crossref  mathscinet  zmath  isi  scopus
    5. Nykyforchyn O., Repovš D., “Idempotent convexity and algebras for the capacity monad and its submonads”, Appl. Categ. Structures, 19:4 (2011), 709–727  crossref  mathscinet  isi  scopus
    6. Repovš D., Zarichnyi M., “Convex hyperspaces of probability measures and extensors in the asymptotic category”, Topology Appl., 158:13 (2011), 1571–1574  crossref  mathscinet  zmath  isi  scopus
    7. Nykyforchyn O., Zarichnyi M., “Open mapping theorems for capacities”, Fund. Math., 211:1 (2011), 1–13  crossref  mathscinet  zmath  isi  scopus
    8. Nykyforchyn O., “Adjoints and monads related to compact lattices and compact Lawson idempotent semimodules”, Order, 29:1 (2012), 193–213  crossref  mathscinet  zmath  isi  scopus
    9. Nykyforchyn O., Repovs D., “L-Convexity and Lattice-Valued Capacities”, J. Convex Anal., 21:1 (2014), 29–52  mathscinet  zmath  isi  elib
    10. Radul T., “Nash equilibrium for binary convexities”, Topol. Methods Nonlinear Anal., 48:2 (2016), 555–565  crossref  zmath  isi  scopus
    11. Nykyforchyn O.R., Hlushak I.D., “Approximation of Capacities With Additive Measures”, Carpathian Math. Publ., 9:1 (2017), 92–97  crossref  mathscinet  zmath  isi
    12. Radul T., “Equilibrium Under Uncertainty With Sugeno Payoff”, Fuzzy Sets Syst., 349 (2018), 64–70  crossref  mathscinet  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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