MB-Representations and Topological Algebras

Bartoszewicz, Artur; Ciesielski, Krzysztof

doi:10.14321/realanalexch.27.2.0749

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The Families Aldo and T A1

Example 4 There Exists a Maximal Almost Disjoint Family1

Introduction1

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Cited by 5 publications

(3 citation statements)

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“…There exists a measurable space X, S, J having the hull property such that LDO = ∅ and, in consequence, T = ∅ (see [1]). For the family ALDO the situation is different.…”

Section: The Families Aldo and T Amentioning

confidence: 99%

On lower density type operators and topologies generated by them

Hejduk¹,

Lindner²,

Loranty³

2018

Filomat

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“…There exists a measurable space X, S, J having the hull property such that LDO = ∅ and, in consequence, T = ∅ (see [1]). For the family ALDO the situation is different.…”

Section: The Families Aldo and T Amentioning

confidence: 99%

On lower density type operators and topologies generated by them

Hejduk¹,

Lindner²,

Loranty³

2018

Filomat

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“…Proof. In [BC,fact 4] it was proved that for every F as in the theorem the algebra S(F) contains F (so it has inner MB-representation) and S 0 (F) = [X] <κ .…”

Section: Example 4 There Exists a Maximal Almost Disjoint Familymentioning

confidence: 99%

Algebras with Inner MB-Representation

Balcerzak

Bartoszewicz

Ciesielski

2004

Real Analysis Exchange

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We investigate algebras of sets, and pairs A, I consisting of an algebra A and an ideal I ⊂ A, that possess an inner MB-representation. We compare inner MB-representability of A, I with several properties of A, I considered by Baldwin. We show that A is inner MBrepresentable if and only if A = S(A\H(A)), where S(•) is a Marczewski operation defined below and H consists of sets that are hereditarily in A. We study the question of uniqueness of the ideal in that representation. 1 The implications Let X be a nonempty set and let F be a nonempty family of nonempty subsets of X. Following the idea of Burstin and Marczewski we define:

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“…This problem has been investigated previously in [3,4,6]. c 2015 Australian Mathematical Publishing Association Inc. 0004-9727/2015 $16.00 [2] Resolvability properties of similar topologies 471 2.…”

Section: Introductionmentioning

confidence: 99%

Resolvability Properties of Similar Topologies

Lindner

2015

Bull. Aust. Math. Soc.

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We demonstrate that many properties of topological spaces connected with the notion of resolvability are preserved by the relation of similarity between topologies. Moreover, many of them can be characterised by the properties of the algebra of sets with nowhere dense boundary and the ideal of nowhere dense sets. We use these results to investigate whether a given pair of an algebra and an ideal is topological.2010 Mathematics subject classification: primary 54A10; secondary 54A05, 11B05, 28A05.

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MB-Representations and Topological Algebras

Cited by 5 publications

References 7 publications

On lower density type operators and topologies generated by them

On lower density type operators and topologies generated by them

Algebras with Inner MB-Representation

Resolvability Properties of Similar Topologies

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