caa a22 4500 445813881 CHVBK 20180317145220.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s11083-010-9161-5 doi (NATIONALLICENCE)springer-10.1007/s11083-010-9161-5 Combinatorics of Thin Posets: Application to Monotone Covering Properties [Elektronische Daten] [Maddalena Bonanzinga, Mikhail Matveev] 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. Springer Science+Business Media B.V., 2010 Tree nationallicence Thin poset nationallicence Lindelöf space nationallicence Monotonically Lindelöf space nationallicence Menger space nationallicence Monotonically Menger space nationallicence Separable space nationallicence First countable space nationallicence Bonanzinga Maddalena Dipartimento di Matematica, Facoltà di Scienze MM.FF.NN., Università di Messina, Viale Fernando Stagno d' Alcontres, 31 98166, Messina, Italy aut Matveev Mikhail Department of Mathematical Sciences, George Mason University, 4400 University Drive, 22030, Fairfax, VA, USA aut Order Springer Netherlands 28/2(2011-07-01), 173-179 0167-8094 28:2<173 2011 28 11083 https://doi.org/10.1007/s11083-010-9161-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11083-010-9161-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bonanzinga Maddalena Dipartimento di Matematica, Facoltà di Scienze MM.FF.NN., Università di Messina, Viale Fernando Stagno d' Alcontres, 31 98166, Messina, Italy aut NATIONALLICENCE 700 1- Matveev Mikhail Department of Mathematical Sciences, George Mason University, 4400 University Drive, 22030, Fairfax, VA, USA aut NATIONALLICENCE 773 0- Order Springer Netherlands 28/2(2011-07-01), 173-179 0167-8094 28:2<173 2011 28 11083 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer