scholarly journals Cardinal invariants of strongly porous sets

2017 ◽  
pp. 1-16
Author(s):  
Osvaldo Guzmán ◽  
Michael Hrušák ◽  
Arturo Martinez-Celis
Keyword(s):  
Cardinal Invariants ◽  
Porous Sets

Cardinal invariants of monotone and porous sets

2012 ◽  
Vol 77 (1) ◽  
pp. 159-173 ◽  
Author(s):  
Michael Hrušák ◽  
Ondřej Zindulka
Keyword(s):  
Metric Space ◽  
Linear Order ◽  
Cantor Set ◽  
Strong Connection ◽  
Cardinal Invariants ◽  
Porous Sets

AbstractA metric space (X, d) ismonotoneif there is a linear order < onXand a constantcsuch thatd(x, y)≤c d(x, z)for allx<y<zinX. We investigate cardinal invariants of theσ-idealMongenerated by monotone subsets of the plane. Since there is a strong connection between monotone sets in the plane and porous subsets of the line, plane and the Cantor set, cardinal invariants of these ideals are also investigated. In particular, we show that non(Mon) ≥mσ-linked, but non(Mon) <mσ-centeredis consistent. Also cov(Mon) <cand cof (N) < cov(Mon) are consistent.

Geometric Cardinal Invariants, Maximal Functions and a Measure Theoretic Pigeonhole Principle

2005 ◽  
Vol 11 (4) ◽  
pp. 517-525
Author(s):  
Juris Steprāns
Keyword(s):  
Harmonic Analysis ◽  
Set Theory ◽  
Harmonic Functions ◽  
Maximal Functions ◽  
Pigeonhole Principle ◽  
Cardinal Invariants ◽  
Geometric Objects

AbstractIt is shown to be consistent with set theory that every set of reals of size ℵ1 is null yet there are ℵ1 planes in Euclidean 3-space whose union is not null. Similar results will be obtained for other geometric objects. The proof relies on results from harmonic analysis about the boundedness of certain harmonic functions and a measure theoretic pigeonhole principle.

CARDINAL INVARIANTS AND SETS OF REALS

1995 ◽  
Vol 21 (1) ◽  
pp. 78
Author(s):  
Bartoszyński
Keyword(s):  
Cardinal Invariants

THE STRUCTURE OF THE σ-IDEAL OF σ-POROUS SETS

1999 ◽  
Vol 25 (1) ◽  
pp. 87
Author(s):  
Zelený
Keyword(s):  
Porous Sets

Converse dual cardinals

2006 ◽  
Vol 71 (1) ◽  
pp. 22-34 ◽  
Author(s):  
Jörg Brendle ◽  
Shuguo Zhang
Keyword(s):  
Natural Numbers ◽  
Cardinal Invariants ◽  
The Continuum

AbstractWe investigate the set (ω) of partitions of the natural numbers ordered by ≤* where A ≤* B if by gluing finitely many blocks of A we can get a partition coarser than B. In particular, we determine the values of a number of cardinals which are naturally associated with the structure ((ω), ≥*), in terms of classical cardinal invariants of the continuum.

Cardinal invariants of infinite groups

1990 ◽  
Vol 30 (3) ◽  
pp. 155-170
Author(s):  
Jörg Brendle
Keyword(s):  
Infinite Groups ◽  
Cardinal Invariants

Cardinal Invariants of l-Topologies

2004 ◽  
Vol 45 (2) ◽  
pp. 241-247
Author(s):  
N. V. Velichko
Keyword(s):  
Cardinal Invariants
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