Some properties of the linear hull of the Erdoes set in [l^2]

• Autorzy: Banach T.
• Języki publikacji: EN

Abstrakty

EN

It is proved that the linear hull L = span E of the Erdoes set E = {(x[i]) [belongs to l^2] [...] x[i] [belongs to] Q for all i} in [l^2] has the following properties: (i) L is linearly homeomorphic to L x L, (ii) L is a countable-dimensional space, (iii) L is an F[sub sigma, delta, sigma]-set in [l^2], (iv) L is a [sigma]Z[sub n]-space for every n [is greater than or equal to] 0, (v) L is not a [sigma]Z[infinity]-space, and (vi) L is ultrabarrelled.

Słowa kluczowe

EN

Borel set; countable-dimensional space; pre-Hilbert space; sigmaZ[sub n]-space; ultrabarrelled space; Z[sub n]-set

PL

kompleksy symplicjalne; rozmaitości; zbiór Borela

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1999
• Tom: Vol. 47, no 4
• Strony: 385--391
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Banach T.

• Department of Mathematics, Lviv University, Universytetska 1, Lviv, 290602, Ukraine

Bibliografia

• [1] S. Banach, Über Metrische Gruppen, Studia Math., 3 (1931) 101-113.
• [2] T. Banakh, Characterization of convex Z-sets in linear metric spaces (in Russian), Funct. Analiz i Prilozh., 28 (1994) 77-79; English transl. in: Funct. Anal. and its Appl., 28 (1994) 285-286.
• [3] T. Banakh, Some problems in infinite-dimensional topology, Matematychni Studii, 8 (1) (1997) 123-125.
• [4] T. Banakh, T. Radul, M. Zarichnyi, Absorbing sets in infinite-dimensional manifolds, VNTL Publishers, Lviv 1996.
• [5] T. Banakh, Kh. Trushchak, Z0-Sets and the disjoint n-cells property in products of ANR's, Matematychni Studii, to be published.
• [6] C. Bessaga, A. Pełczyński, Selected topics in infinite-dimensional topology, PWN, Warsaw 1975.
• [7] R. Daverman, J. J. Walsh, Čech homology characterizations of infinite-dimensional manifolds, Amer. J. Math., 103 (1981) 411-435.
• [8] T. Dobrowolski, The compact Z-set property in convex sets, Top. Appl., 23 (1986) 163-172.
• [9] T. Dobrowolski, J. Mogilski, Problems on topological classification of incomplete metric spaces, in: Open problems in topology, eds.: J. van Mill, G. M. Reed, Elsevier Sci., B.V., Amsterdam 1990, 409-429.
• [10] G. A. Edwards, Functional analysis, NY etc. 1965.
• [11] R. Engelking, General Topology, PWN, Warsaw 1977.
• [12] V. V. Fedorchuk, A. Chigogidze, Absolute retracts and infinite-dimen-sional manifolds (in Russian), Nauka, Moscow 1992.
• [13] N. S. Kroonenberg, Characterization of finite-dimensional Z-sets, Proc. Amer. Math. Soc., 83 (1977) 495-552.