OPEN GRAPHS AND TUKEY ORDER

Authors:	Todorčević, Stevo
Affiliations:	Mathematics Mathematical Institute of the Serbian Academy of Sciences and Arts
Title:	OPEN GRAPHS AND TUKEY ORDER
Journal:	Proceedings of the American Mathematical Society
Volume:	153
First page:	4025
Last page:	4039
Issue Date:	2025
Rank:	M22
ISSN:	0002-9939
DOI:	10.1090/proc/17320
Abstract:	The two alternatives G ≤ Kℵ0 and Kℵ1 ≤ G of the Open Graph Dichotomy are explored here for a natural class of graphs associated to points x in topological spaces X. This is then used in finding Tukey restrictions on the neighbourhood filters of points x guaranteeing that they have strong properties of sequential convergence. This paper can be seen as natural continuation of Todorcevic [Fund. Math. 267 (2024), pp. 181-194] that gives a Tukey theory interpretations of alternatives of another combinatorial dichotomy.
Keywords:	Fréchet spaces \| Open Graph Dichotomys \| Tukey reductions
Publisher:	American Mathematical Society

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