Calibres, compacta and diagonals

Paul Gartside, and Jeremiah Morgan. "Calibres, compacta and diagonals." Fundamenta Mathematicae 232.1 (2016): 1-19. <http://eudml.org/doc/282982>.

@article{PaulGartside2016,
abstract = {For a space Z let 𝒦(Z) denote the partially ordered set of all compact subspaces of Z under set inclusion. If X is a compact space, Δ is the diagonal in X², and 𝒦(X²∖Δ) has calibre (ω₁,ω), then X is metrizable. There is a compact space X such that X²∖Δ has relative calibre (ω₁,ω) in 𝒦(X²∖Δ), but which is not metrizable. Questions of Cascales et al. (2011) concerning order constraints on 𝒦(A) for every subspace of a space X are answered.},
author = {Paul Gartside, Jeremiah Morgan},
journal = {Fundamenta Mathematicae},
language = {eng},
number = {1},
pages = {1-19},
title = {Calibres, compacta and diagonals},
url = {http://eudml.org/doc/282982},
volume = {232},
year = {2016},
}

TY - JOUR
AU - Paul Gartside
AU - Jeremiah Morgan
TI - Calibres, compacta and diagonals
JO - Fundamenta Mathematicae
PY - 2016
VL - 232
IS - 1
SP - 1
EP - 19
AB - For a space Z let 𝒦(Z) denote the partially ordered set of all compact subspaces of Z under set inclusion. If X is a compact space, Δ is the diagonal in X², and 𝒦(X²∖Δ) has calibre (ω₁,ω), then X is metrizable. There is a compact space X such that X²∖Δ has relative calibre (ω₁,ω) in 𝒦(X²∖Δ), but which is not metrizable. Questions of Cascales et al. (2011) concerning order constraints on 𝒦(A) for every subspace of a space X are answered.
LA - eng
UR - http://eudml.org/doc/282982
ER -