Measures on compact HS spaces

Mirna Džamonja; Kenneth Kunen

Fundamenta Mathematicae (1993)

  • Volume: 143, Issue: 1, page 41-54
  • ISSN: 0016-2736

Abstract

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We construct two examples of a compact, 0-dimensional space which supports a Radon probability measure whose measure algebra is isomorphic to the measure algebra of 2 ω 1 . The first construction uses ♢ to produce an S-space with no convergent sequences in which every perfect set is a G δ . A space with these properties must be both hereditarily normal and hereditarily countably paracompact. The second space is constructed under CH and is both HS and HL.

How to cite

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Džamonja, Mirna, and Kunen, Kenneth. "Measures on compact HS spaces." Fundamenta Mathematicae 143.1 (1993): 41-54. <http://eudml.org/doc/211991>.

@article{Džamonja1993,
abstract = {We construct two examples of a compact, 0-dimensional space which supports a Radon probability measure whose measure algebra is isomorphic to the measure algebra of $2^\{ω_1\}$. The first construction uses ♢ to produce an S-space with no convergent sequences in which every perfect set is a $G_δ$. A space with these properties must be both hereditarily normal and hereditarily countably paracompact. The second space is constructed under CH and is both HS and HL.},
author = {Džamonja, Mirna, Kunen, Kenneth},
journal = {Fundamenta Mathematicae},
keywords = {HS spaces; Radon probability measure; compact space},
language = {eng},
number = {1},
pages = {41-54},
title = {Measures on compact HS spaces},
url = {http://eudml.org/doc/211991},
volume = {143},
year = {1993},
}

TY - JOUR
AU - Džamonja, Mirna
AU - Kunen, Kenneth
TI - Measures on compact HS spaces
JO - Fundamenta Mathematicae
PY - 1993
VL - 143
IS - 1
SP - 41
EP - 54
AB - We construct two examples of a compact, 0-dimensional space which supports a Radon probability measure whose measure algebra is isomorphic to the measure algebra of $2^{ω_1}$. The first construction uses ♢ to produce an S-space with no convergent sequences in which every perfect set is a $G_δ$. A space with these properties must be both hereditarily normal and hereditarily countably paracompact. The second space is constructed under CH and is both HS and HL.
LA - eng
KW - HS spaces; Radon probability measure; compact space
UR - http://eudml.org/doc/211991
ER -

References

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  1. [1] V. V. Fedorchuk, On the cardinality of hereditarily separable compact spaces, Dokl. Akad. Nauk SSSR 222 (1975), 302-305 (in Russian). Zbl0331.54029
  2. [2] D. Fremlin, Consequences of Martin's Axiom, Cambridge University Press, 1984. Zbl0551.03033
  3. [3] A. Hajnal and I. Juhász, On first countable non-Lindelöf S-spaces, in: Colloq. Math. Soc. János Bolyai 10, North-Holland, 1975, 837-852. 
  4. [4] R. Haydon, On dual L 1 -spaces and injective bidual Banach spaces, Israel J. Math. 31 (1978), 142-152. Zbl0407.46018
  5. [5] I. Juhász, K. Kunen and M. E. Rudin, Two more hereditarily separable non-Lindelöf spaces, Canad. J. Math. 28 (1976), 998-1005. Zbl0336.54040
  6. [6] K. Kunen, A compact L-space under CH, Topology Appl. 12 (1981), 283-287. 
  7. [7] D. Maharam, On homogeneous measure algebras, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 108-111. Zbl0063.03723
  8. [8] J. Roitman, Basic S and L, in: Handbook of Set-Theoretic Topology, K. Kunen and J. Vaughan (eds.), North-Holland, 1984, 295-326. 

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