Abstract
A variant of the Bourgin-Yang theorem for
A variant of the Bourgin-Yang theorem for
S. A. Antonyan, “Retracts in categories of -spaces,” Izvestiya Akademii Nauk Armyanskoĭ SSR. Seriya Matematika, vol. 15, no. 5, pp. 365–378, 1980, English translation in: Soviet Journal of Contemporary Mathematical Analysis \textbf{15} (1980), 30–43.
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis, John Wiley & Sons, New York, 1984.
View at: Zentralblatt MATH | MathSciNetT. Bartsch, Topological Methods for Variational Problems with Symmetries, vol. 1560 of Lecture Notes in Mathematics, Springer, Berlin, 1993.
View at: Zentralblatt MATH | MathSciNetV. Benci, “On critical point theory for indefinite functionals in the presence of symmetries,” Transactions of the American Mathematical Society, vol. 274, no. 2, pp. 533–572, 1982.
View at: Google Scholar | Zentralblatt MATH | MathSciNetD. G. Bourgin, “On some separation and mapping theorems,” Commentarii Mathematici Helvetici, vol. 29, pp. 199–214, 1955.
View at: Google Scholar | Zentralblatt MATH | MathSciNetG. Bredon, Introduction to Compact Transformation Groups, Academic Press, New York, 1972.
View at: MathSciNetZ. Dzedzej, “Equivariant selections and approximations,” in Topological Methods in Nonlinear Analysis, pp. 25–31, Gdansk Scientific Society, Gdansk, 1997.
View at: Google ScholarB. D. Gel'man, “The Borsuk-Ulam theorem in infinite-dimensional Banach spaces,” Sbornik: Mathematics, vol. 193, no. 1, pp. 83–91, 2002.
View at: Google Scholar | Zentralblatt MATH | MathSciNetB. D. Gel'man, “An infinite-dimensional version of the Borsuk-Ulam theorem,” Functional Analysis and Its Applications, vol. 38, no. 4, pp. 1–5, 2004.
View at: Google Scholar | Zentralblatt MATH | MathSciNetP. Holm and E. H. Spanier, “Involutions and Fredholm maps,” Topology, vol. 10, no. 3, pp. 203–218, 1971.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ. Ize and A. Vignoli, Equivariant Degree Theory, vol. 8 of De Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter, Berlin, 2003.
View at: Zentralblatt MATH | MathSciNetW. Krawcewicz and J. Wu, Theory of Degrees with Applications to Bifurcations and Differential Equations, John Wiley & Sons, New York, 1997.
View at: Zentralblatt MATH | MathSciNetA. Kushkuley and Z. I. Balanov, Geometric Methods in Degree Theory for Equivariant Maps, vol. 1632 of Lecture Notes in Mathematics, Springer, Berlin, 1996.
View at: Zentralblatt MATH | MathSciNetJ. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, vol. 74 of Applied Mathematical Sciences, Springer, New York, 1989.
View at: Zentralblatt MATH | MathSciNetE. Michael, “Continuous selections I,” Annals of Mathematics, vol. 63, pp. 361–382, 1956.
View at: Google Scholar | Zentralblatt MATH | MathSciNetW. Rudin, Functional Analysis, McGraw-Hill, New York, 2nd edition, 1991.
View at: Zentralblatt MATH | MathSciNetH. Steinlein, “Borsuk's antipodal theorem and its generalizations and applications: a survey,” in Topological Methods in Nonlinear Analysis, A. Granas, Ed., vol. 95 of Sém Mathematics Sup., pp. 166–235, Presses de l ' Université of Montréal, Montreal, 1985.
View at: Google Scholar | Zentralblatt MATH | MathSciNetI. A. Wolf, Spaces of Constant Curvature, McGraw-Hill, New York, 1967.
View at: Zentralblatt MATH | MathSciNetC.-T. Yang, “On theorems of Borsuk-Ulam, Kakutani-Yamabe-Yujobo and Dyson I,” Annals of Mathematics, vol. 60, pp. 262–282, 1954.
View at: Google Scholar | Zentralblatt MATH | MathSciNetD. P. Zhelobenko, Introduction to Representation Theory, Factorial Press, Moscow, 2001.
D. P. Zhelobenko and A. I. Shtern, Representations of Lie Groups, Nauka, Moscow, 1983.
View at: Zentralblatt MATH | MathSciNet