The Uniform Effros Property and Local Homogeneity
Por:
Macias, Sergio
Publicada:
1 ago 2023
Categoría:
Mathematics (miscellaneous)
Resumen:
Kathryn F. Porter wrote a nice paper about several definitions of local
homogeneity [Local homogeneity, JP Journal of Geometry and Topology 9
(2009), 129-136]. In this paper, she mentions that G. S. Ungar defined a
uniformly locally homogeneous space [Local homogeneity, Duke Math. J.
34 (1967), 693-700]. We realized that this notion is very similar to
what we call the uniform property of Effros [On Jones' set function T
and the property of Kelley for Hausdorff continua, Topology Appl. 226
(2017), 51-65]. Here, we compare the uniform property of Effros with the
uniform local homogeneity. We also consider other definitions of local
homogeneity given in Porter's paper and compare them with the uniform
property of Effros. We show that in the presence of compactness, the
uniform property of Effros is equivalent to uniform local homogeneity
and the local homogeneity according to Ho. With this result, we can
change the hypothesis of the uniform property of Effros in Jones' and
Prajs' decomposition theorems to uniform local homogeneity and local
homogeneity according to Ho. We add to these two results the fact that
the corresponding quotient space also has the uniform property of
Effros.
Filiaciones:
Macias, Sergio:
Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, Circuito Exterior, CDMX, Mexico, C. P. 04510, Mexico
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