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Combinatorics of Thin Posets: Application to Monotone Covering Properties

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Abstract

A class of posets, called thin posets, is introduced, and it is shown that every thin poset can be covered by a finite family of trees. This fact is used to show that (within ZFC) every separable monotonically Menger space is first countable. This contrasts with the previously known fact that under CH there are countable monotonically Lindelöf spaces which are not first countable.

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Authors and Affiliations

  1. Dipartimento di Matematica, Facoltà di Scienze MM.FF.NN., Università di Messina, Viale Fernando Stagno d’ Alcontres, 31 98166, Messina, Italy

    Maddalena Bonanzinga

  2. Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, VA, 22030, USA

    Mikhail Matveev

Authors
  1. Maddalena Bonanzinga
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  2. Mikhail Matveev
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Correspondence to Mikhail Matveev.

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Bonanzinga, M., Matveev, M. Combinatorics of Thin Posets: Application to Monotone Covering Properties. Order 28, 173–179 (2011). https://doi.org/10.1007/s11083-010-9161-5

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  • DOI: https://doi.org/10.1007/s11083-010-9161-5

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