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Mat. Sb., 1991, Volume 182, Number 9, Pages 1261–1280 (Mi msb1358)  

This article is cited in 5 scientific papers (total in 5 papers)

Absolute extensors and the geometry of multiplication of monads in the category of compacta

M. M. Zarichnyi

Ivan Franko National University of L'viv

Abstract: An investigation is made of the geometry of the multiplication mappings $\mu X$ for monads $\mathbf T=(t,\eta,\mu)$ whose functorial parts are (weakly) normal (in the sense of Shchepin) functors acting in the category of compacta. A characterization is obtained for a power monad as the only normal monad such that the multiplication mapping $\mu I^\tau$ is soft for some $\tau>\omega_1$. It is proved that the multiplication mappings $\mu_GX$ and $\mu_NX$ of the inclusion hyperspace monad and the monad of complete chained systems are homeomorphic to trivial Tychonoff fibrations for openly generated continua $X$ that are homogeneous with respect to character.

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English version:
Mathematics of the USSR-Sbornik, 1993, 74:1, 9–27

Bibliographic databases:

UDC: 515.12
MSC: Primary 54B30, 54B20; Secondary 18C15, 18B30
Received: 11.09.1990

Citation: M. M. Zarichnyi, “Absolute extensors and the geometry of multiplication of monads in the category of compacta”, Mat. Sb., 182:9 (1991), 1261–1280; Math. USSR-Sb., 74:1 (1993), 9–27

Citation in format AMSBIB
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\by M.~M.~Zarichnyi
\paper Absolute extensors and the geometry of multiplication of monads in the category of compacta
\jour Mat. Sb.
\yr 1991
\vol 182
\issue 9
\pages 1261--1280
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1133568}
\zmath{https://zbmath.org/?q=an:0813.54008}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1993SbMat..74....9Z}
\transl
\jour Math. USSR-Sb.
\yr 1993
\vol 74
\issue 1
\pages 9--27
\crossref{https://doi.org/10.1070/SM1993v074n01ABEH003331}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993KQ22500002}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Radul T., “On the Barycenter Mapping for Probability-Measures”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1994, no. 1, 3–6  mathscinet  zmath  isi
    2. M. M. Zarichnyi, T. N. Radul, “Monads in the category of compacta”, Russian Math. Surveys, 50:3 (1995), 549–574  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Radul T., “On Barycentrically Soft Compacta”, Fundam. Math., 148:1 (1995), 27–33  mathscinet  zmath  isi
    4. M. M. Zarichnyi, “Spaces and maps of idempotent measures”, Izv. Math., 74:3 (2010), 481–499  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. Karchevs'ka L.I., “On Geometric Properties of Functors of Positive-Homogenous and Semiadditive Functionals”, Ukr. Math. J., 62:10 (2011), 1567–1576  crossref  mathscinet  isi
  • Математический сборник - 1991 Sbornik: Mathematics (from 1967)
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