Glasnik Matematicki, Vol. 55, No. 2 (2020), 367-373.

ČECH SYSTEMS AND APPROXIMATE INVERSE SYSTEMS

Vlasta Matijević and Leonard R. Rubin

Department of Mathematics, Faculty of Science, University of Split, 21 000 Split, Croatia
e-mail: vlasta@pmfst.hr

Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019, USA
e-mail: lrubin@ou.edu

Abstract.   We generalize a result of the first author who proved that the Čech system of open covers of a Hausdorff arc-like space cannot induce an approximate system of the nerves of these covers under any choices of the meshes and the projections.

2010 Mathematics Subject Classification.   54B35, 55N05

Key words and phrases.   Approximate inverse system, arc-like, Čech system, normal cover, perfect space, simple chain

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https://doi.org/10.3336/gm.55.2.12

References:

  1. S. Mardešić, On approximate inverse systems and resolutions, Fund. Math. 142 (1993), 241-255.
    MathSciNet     CrossRef

  2. S. Mardešić and T. Watanabe, Approximate resolutions of spaces and mappings, Glas. Mat. Ser. III 24(44) (1989), 587-637.
    MathSciNet    

  3. V. Matijević, Čech system does not induce approximate systems, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 21(532) (2017), 169-177.
    MathSciNet     CrossRef

  4. V. Matijević and N. Uglešić, A new approach to the theory of approximate systems, preprint.
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