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

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

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
\Bibitem{Zar91} \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 \mathnet{http://mi.mathnet.ru/msb1358} \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
2. M. M. Zarichnyi, T. N. Radul, “Monads in the category of compacta”, Russian Math. Surveys, 50:3 (1995), 549–574
3. Radul T., “On Barycentrically Soft Compacta”, Fundam. Math., 148:1 (1995), 27–33
4. M. M. Zarichnyi, “Spaces and maps of idempotent measures”, Izv. Math., 74:3 (2010), 481–499
5. Karchevs'ka L.I., “On Geometric Properties of Functors of Positive-Homogenous and Semiadditive Functionals”, Ukr. Math. J., 62:10 (2011), 1567–1576
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