Abstract

RINCON-VILLAMIZAR, Michael A.. A proof of Holsztyński theorem. Integración - UIS [online]. 2018, vol.36, n.1, pp.59-65. ISSN 0120-419X.  https://doi.org/10.18273/revint.v36n1-2018005.

For a compact Hausdorff space, we denote by C(K) the Banach space of continuous functions defined in K with values in R or C. A well known result in Banach spaces of continuous functions is the Holsztyński theorem which establishes that if C(K) is isometric to a subspace of C(S), then K is a continuous image of S. The aim of this paper is to give an alternative proof of this result for extremely regular subspaces of C(K).

MSC2010: 46B03, 46E15, 46E40, 46B25.

Keywords : C(K) Banach spaces; Banach-Stone theorem.

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