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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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ISSN
2391-5455
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Volume 11, Issue 1

Issues

Volume 13 (2015)

A spectral characterization of skeletal maps

Taras Banakh
  • Faculty of Mechanics and Mathematics, Ivan Franko National University of Lviv, Universytetska 1, Lviv, 79000, Ukraine
  • Instytut Matematyki, Jan Kochanowski University, Świętokrzyska 15, Kielce, Poland
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/ Andrzej Kucharski / Marta Martynenko
  • Faculty of Mechanics and Mathematics, Ivan Franko National University of Lviv, Universytetska 1, Lviv, 79000, Ukraine
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Published Online: 2012-10-24 | DOI: https://doi.org/10.2478/s11533-012-0058-y

Abstract

We prove that a map between two realcompact spaces is skeletal if and only if it is homeomorphic to the limit map of a skeletal morphism between ω-spectra with surjective limit projections.

MSC: 54B35; 54C10

Keywords: Skeletal map; Inverse spectrum

  • [1] Banakh T., Kucharski A., Martynenko M., On functors preserving skeletal maps and skeletally generated compacta, preprint available at http://arxiv.org/abs/1108.4197 Web of ScienceGoogle Scholar

  • [2] Chigogidze A., Inverse Spectra, North-Holland Math. Library, 53, North-Holland Publishing, Amsterdam, 1996 http://dx.doi.org/10.1016/S0924-6509(96)80001-8CrossrefGoogle Scholar

  • [3] Engelking R., General Topology, Sigma Ser. Pure Math., 6, Heldermann, Berlin, 1989 Google Scholar

  • [4] Fedorchuk V., Chigogidze A.Ch., Absolute Retracts and Infinite-Dimensional Manifolds, Nauka, Moscow, 1992 (in Russian) Google Scholar

  • [5] Mioduszewski J., Rudolf L., H-Closed and Extremally Disconnected Hausdorff Spaces, Dissertationes Math. (Rozprawy Mat.), 66, Polish Academy of Sciences, Warsaw, 1969 Google Scholar

About the article

Published Online: 2012-10-24

Published in Print: 2013-01-01


Citation Information: Open Mathematics, Volume 11, Issue 1, Pages 161–169, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-012-0058-y.

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© 2012 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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