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On structural numbers of topological spaces

  • Vitalij A. Chatyrko und Alexandre Karassev EMAIL logo
Veröffentlicht/Copyright: 24. Oktober 2025
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Abstract

Zero-dimensional structural numbers Z0ind  and Z0dim  w.r.t. dimensions ind and dim were introduced by Georgiou, Hattori, Megaritis, and Sereti. Somewhat similarly, we define structural numbers Sn𝒜 for different subclasses 𝒜 of the class of hereditarily normal T1-spaces. In particular, if dim denotes the class of metrizable spaces Z with dim Z = 0; we show that:

  1. for any metrizable space X with dim X = n ≥ 0, we have 1SnMdimXn+1;

  2. for any countable-dimensional metrizable space Y, we have 1SnMdimY0.

Funding statement: The second author was partially supported by NSERC Discovery Development Grant.

Acknowledgement

The authors thank the anonymous referees for valuable suggestions that helped to improve the paper.

  1. (Communicated by David Buhagiar)

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Received: 2025-02-22
Accepted: 2025-05-02
Published Online: 2025-10-24
Published in Print: 2025-10-27

© 2025 Mathematical Institute Slovak Academy of Sciences

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Heruntergeladen am 26.10.2025 von https://www.degruyterbrill.com/document/doi/10.1515/ms-2025-0090/pdf
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