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Mat. Sb., 2002, Volume 193, Number 1, Pages 83–92 (Mi msb621)  

This article is cited in 9 scientific papers (total in 9 papers)

Borsuk–Ulam theorem in infinite-dimensional Banach spaces

B. D. Gel'man

Voronezh State University

Abstract: The well-known classical Borsuk–Ulam theorem has a broad range of applications to various problems. Its generalization to infinite-dimensional spaces runs across substantial difficulties because its statement is essentially finite-dimensional. A result established in the paper is a natural generalization of the Borsuk–Ulam theorem to infinite-dimensional Banach spaces. Applications of this theorem to various problems are discussed.

DOI: https://doi.org/10.4213/sm621

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English version:
Sbornik: Mathematics, 2002, 193:1, 83–91

Bibliographic databases:

UDC: 517.988.6
MSC: Primary 55M20, 46B20; Secondary 93C23
Received: 30.10.2000 and 24.04.2001

Citation: B. D. Gel'man, “Borsuk–Ulam theorem in infinite-dimensional Banach spaces”, Mat. Sb., 193:1 (2002), 83–92; Sb. Math., 193:1 (2002), 83–91

Citation in format AMSBIB
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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. B. D. Gel'man, “An Infinite-Dimensional Version of the Borsuk–Ulam Theorem”, Funct. Anal. Appl., 38:4 (2004), 239–242  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Antonyan S.A., Balanov Z.I., Gel'man B.D., “Bourgin-Yang-type theorem for $a$-compact perturbations of closed operators. Part I. The case of index theories with dimension property”, Abstr. Appl. Anal., 2006, 78928, 13 pp.  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    3. Prykarpats'kyi A.K., “An infinite-dimensional Borsuk-Ulam-type generalization of the Leray-Schauder fixed-point theorem and some applications”, Ukrainian Math. J., 60:1 (2008), 114–120  crossref  mathscinet  isi  scopus  scopus  scopus
    4. Volovikov A.Yu., “Borsuk-Ulam implies Brouwer: A direct construction revisited”, Amer. Math. Monthly, 115:6 (2008), 553–556  crossref  mathscinet  zmath  isi  elib
    5. Prykarpatsky A.K., Blackmore D., “A solution set analysis of a nonlinear operator equation using a Leray-Schauder type fixed point approach”, Topology, 48:2–4 (2009), 182–185  crossref  mathscinet  zmath  isi  scopus
    6. Gelman B.D., Zhuk N.M., “O beskonechnomernoi versii teoremy borsuka-ulama dlya mnogoznachnykh otobrazhenii”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika, 2011, no. 2, 78–84  zmath  elib
    7. Gelman B.D., Rydanova S.S., “Ob operatornykh uravneniyakh s syurektivnymi operatorami”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika, 2012, no. 1, 93–93  mathscinet  zmath  elib
    8. B. D. Gel'man, “A version of the infinite-dimensional Borsuk-Ulam theorem for multivalued maps”, Sb. Math., 207:6 (2016), 841–853  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    9. B. D. Gelman, “O teoreme Borsuka–Ulama dlya lipshitsevykh otobrazhenii v beskonechnomernom prostranstve”, Funkts. analiz i ego pril., 53:1 (2019), 79–83  mathnet  crossref  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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