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Article

Holický, Petr
Binormality of Banach spaces. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 38 (1997), issue 2, pp. 279-282
MSC: 46B20, 46B28, 54E55 | MR 1455495 | Zbl 0886.46012
Keywords:
binormality; Luzin-Menchoff property; Banach space; weak topology
Summary:
We study binormality, a separation property of spaces endowed with two topologies known in the real analysis as the Luzin-Menchoff property. The main object of our interest are Banach spaces with their norm and weak topologies. We show that every separable Banach space is binormal and the space $\ell^{\infty}$ is not binormal.
References:
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[K] Kelly J.C.: Bitopological spaces. Proc. London Math. Soc. 13 (1963), 71-89. MR 0143169 | Zbl 0107.16401
[LMZ] Lukeš J., Malý J., Zajíček L.: Fine Topology Methods in Real Analysis and Potential Theory. Lecture Notes in Mathematics 1189 (1986), Springer-Verlag Berlin, Heidelberg, New York, London, Paris, Tokyo. MR 0861411
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