Topological Structure of Non-separable Sigma-locally Compact Convex Sets

• Autorzy: Banakh I. , Banakh T. , Koshino K.

Identyfikatory

DOI

10.4064/ba61-2-8

• Języki publikacji: EN

Abstrakty

EN

For an infinite cardinal K let l₂ (K) be the linear hull of the standard othonormal base of the Hilbert space l₂(K) of density K. We prove that a non-separable convex subset X of density K = dens(X) in a locally convex linear metric space is homeomorphic to the space.[...]

Słowa kluczowe

EN

convex set; pre-Hilbert space; homeomorphism

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2013
• Tom: Vol. 61, no 2
• Strony: 149--153
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Banakh I.

• Institute for Applied Problems of Mechanics and Mathematics of Ukrainian Academy of Sciences Naukova 3b Lviv, Ukraine

autor

Banakh T.

• Ivan Franko National University of Lviv Lviv, Ukraine
• Jan Kochanowski University Kielce, Poland

autor

Koshino K.

• Doctoral Program in Mathematics Graduate School of Pure and Applied Sciences University of Tsukuba Tsukuba, 305-8571, Japan

Bibliografia

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• [3] T. Banakh, T. Radul and M. Zarichnyi, Absorbing Sets in Infinite-Dimensional Manifolds, VNTL Publ., Lviv, 1996, 240 pp.
• [4] C. Bessaga and A. Pełczynski, Selected Topics in Infinite-Dimensional Topology, PWN, Warszawa, 1975.
• [5] D. Curtis, T. Dobrowolski and J. Mogilski, Some applications of the topological characterizations of the sigma-compact spaces l2 f and Σ, Trans. Amer. Math. Soc. 284 (1984), 837–846.
• [6] T. Dobrowolski, The compact Z-set property in convex sets, Topology Appl. 23(1986), 163–172.
• [7] K. Koshino, Characterizing non-separable sigma-locally compact infinite-dimensional manifolds and its applications, J. Math. Soc. Japan, to appear.
• [8] K. Koshino, The topological types of non-separable sigma-locally compact convex sets, preprint, 2013; included in PhD dissertation, Univ. of Tsukuba, 2014.
• [9] K. Sakai and M. Yaguchi, Characterizing manifolds modeled on certain dense subspaces of non-separable Hilbert spaces, Tsukuba J. Math. 27 (2003), 143–159.
• [10] J. West, The ambient homeomorphy of an incomplete subspace of infinite-dimensional Hilbert spaces, Pacific J. Math. 34 (1970) 257–267.