A spectral characterization of skeletal maps

Taras Banakh; Andrzej Kucharski; Marta Martynenko

Open Mathematics (2013)

  • Volume: 11, Issue: 1, page 161-169
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Taras Banakh, Andrzej Kucharski, and Marta Martynenko. "A spectral characterization of skeletal maps." Open Mathematics 11.1 (2013): 161-169. <http://eudml.org/doc/269504>.

@article{TarasBanakh2013,
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.},
author = {Taras Banakh, Andrzej Kucharski, Marta Martynenko},
journal = {Open Mathematics},
keywords = {Skeletal map; Inverse spectrum; skeletal map; inverse spectrum},
language = {eng},
number = {1},
pages = {161-169},
title = {A spectral characterization of skeletal maps},
url = {http://eudml.org/doc/269504},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Taras Banakh
AU - Andrzej Kucharski
AU - Marta Martynenko
TI - A spectral characterization of skeletal maps
JO - Open Mathematics
PY - 2013
VL - 11
IS - 1
SP - 161
EP - 169
AB - 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.
LA - eng
KW - Skeletal map; Inverse spectrum; skeletal map; inverse spectrum
UR - http://eudml.org/doc/269504
ER -

References

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  1. [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 Zbl1267.18003
  2. [2] Chigogidze A., Inverse Spectra, North-Holland Math. Library, 53, North-Holland Publishing, Amsterdam, 1996 http://dx.doi.org/10.1016/S0924-6509(96)80001-8 
  3. [3] Engelking R., General Topology, Sigma Ser. Pure Math., 6, Heldermann, Berlin, 1989 
  4. [4] Fedorchuk V., Chigogidze A.Ch., Absolute Retracts and Infinite-Dimensional Manifolds, Nauka, Moscow, 1992 (in Russian) Zbl0762.54017
  5. [5] Mioduszewski J., Rudolf L., H-Closed and Extremally Disconnected Hausdorff Spaces, Dissertationes Math. (Rozprawy Mat.), 66, Polish Academy of Sciences, Warsaw, 1969 Zbl0204.22404

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