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RESOLVABILITY OF MEASURABLE SPACES

Part of: Classical measure theory Generalities

Published online by Cambridge University Press:  11 January 2016

GRAŻYNA HORBACZEWSKA  and
SEBASTIAN LINDNER
GRAŻYNA HORBACZEWSKA*
Affiliation:
Department of Mathematics and Computer Science, University of Lodz, Banacha 22, 90 238 Lodz, Poland email [email protected]
SEBASTIAN LINDNER
Affiliation:
Department of Mathematics and Computer Science, University of Lodz, Banacha 22, 90 238 Lodz, Poland email [email protected]
*
✉[email protected]
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Abstract

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We consider a special kind of structure resolvability and irresolvability for measurable spaces and discuss analogues of the criteria for topological resolvability and irresolvability.

Keywords

resolvabilityirresolvabilityalgebra of setsideal of setsMarczewski–Burstin representation

MSC classification

Primary: 28A05: Classes of sets (Borel fields, $sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets
Secondary: 54A10: Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) 06E25: Boolean algebras with additional operations (diagonalizable algebras, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 94 , Issue 1 , August 2016 , pp. 70 - 79
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

Balcerzak, M., Bartoszewicz, A. and Ciesielski, K., ‘Algebras with inner MB-representation’, Real Anal. Exchange 29(1) (2003–2004), 265–273.CrossRefGoogle Scholar
Balcerzak, M., Bartoszewicz, A. and Koszmider, P., ‘On Marczewski–Burstin representable algebras’, Colloq. Math. 99(1) (2004), 55–60.CrossRefGoogle Scholar
Balcerzak, M., Bartoszewicz, A., Rzepecka, J. and Wronski, S., ‘Marczewski fields and ideals’, Real Anal. Exchange 26(2) (2000–2001), 703–715.CrossRefGoogle Scholar
Baldwin, S., ‘The Marczewski hull property and complete Boolean algebras’, Real Anal. Exchange 28(2) (2002–2003), 415–428.CrossRefGoogle Scholar
Bartoszewicz, A., Filipczak, M., Kowalski, A. and Terepeta, M., ‘On similarity between topologies’, Cent. Eur. J. Math. 12(4) (2014), 603–610.Google Scholar
Ceder, J. G., ‘On maximally resolvable spaces’, Fund. Math. 55 (1964), 87–93.CrossRefGoogle Scholar
Elkin, A. G., ‘Resolvable spaces which are not maximally resolvable’, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 24 (1969), 66–70.Google Scholar
Hewitt, E., ‘A problem of set-theoretic topology’, Duke Math. J. 10 (1943), 309–333.CrossRefGoogle Scholar
Horbaczewska, G., ‘Resolvability of abstract density topologies in ℝ n generated by lower or almost lower density operators’, Tatra Mt. Math. Publ. 62 (2015), 175–181.Google Scholar
Horbaczewska, G., Karasińska, A. and Wagner-Bojakowska, E., ‘Properties of the 𝜎-ideal of microscopic sets’, in: Traditional and Present-day Topics in Real Analysis (Łódź University Press, Łódź, 2013), 325–343.Google Scholar
Jiménez, R. and Malykhin, V. I., ‘Structure resolvability’, Comment. Math. Univ. Carolin. 39(2) (1998), 379–387.Google Scholar
Lindner, S., ‘Resolvability properties of similar topologies’, Bull. Aust. Math. Soc. 92(3) (2015), 470–477.CrossRefGoogle Scholar