Free sets for nowhere-dense set mappings

1981 ◽  
Vol 39 (1-2) ◽  
pp. 167-176 ◽  
Author(s):  
Uri Avraham
Keyword(s):  
Set Mappings ◽  
Free Sets ◽  
Nowhere Dense Set ◽  
Dense Set

Nowhere dense set mappings on the generalized linear continua

Order ◽  
1990 ◽  
Vol 7 (2) ◽  
pp. 179-182
Author(s):  
Kandasamy Muthuvel
Keyword(s):  
Set Mappings ◽  
Nowhere Dense Set ◽  
Dense Set

Analytic Functions with an Irregular Linearly Measurable Set of Singular Points

1952 ◽  
Vol 4 ◽  
pp. 424-435 ◽  
Author(s):  
I. E. Glover
Keyword(s):  
Imaginary Part ◽  
Analytic Functions ◽  
Singular Points ◽  
Definite Integrals ◽  
Singular Sets ◽  
Dense Point ◽  
Point Set ◽  
Dense Point Set ◽  
Nowhere Dense Set ◽  
Dense Set

V. V. Golubev, in his study [6], has constructed, by using definite integrals, various examples of analytic functions having a perfect nowhere-dense set of singular points. These functions were shown to be single-valued with a bounded imaginary part. In attempting to extend his work to the problem of constructing analytic functions having perfect, nowhere-dense singular sets under quite general conditions, he posed the following question: Given an arbitrary, perfect, nowhere-dense point-set E of positive measure in the complex plane, is it possible to construct, by passing a Jordan curve through E and by using definite integrals, an example of a single-valued analytic function, which has E as its singular set, with its imaginary part bounded.

Two consistency results on set mappings

2000 ◽  
Vol 65 (1) ◽  
pp. 333-338 ◽  
Author(s):  
Péter Komjáth ◽  
Saharon Shelah
Keyword(s):  
Natural Number ◽  
Consistency Results ◽  
Set Mappings ◽  
Free Sets

AbstractIt is consistent that there is a set mapping from the four-tuples of ωn into the finite subsets with no free subsets of size tn for some natural number tn. For any n < ω it is consistent that there is a set mapping from the pairs of ωn into the finite subsets with no infinite free sets. For any n < ω it is consistent that there is a set mapping from the pairs of ωn into ωn with no uncountable free sets.

On a combinatorial principle of Hajnal and Komjáth

1986 ◽  
Vol 51 (4) ◽  
pp. 1056-1060 ◽  
Author(s):  
Dan Velleman
Keyword(s):  
General Principle ◽  
Cardinal Number ◽  
Order Type ◽  
Infinite Cardinal ◽  
Combinatorial Principle ◽  
Mahlo Cardinal ◽  
One Step ◽  
Set Mappings ◽  
Free Sets

In their paper [3], Hajnal and Komjáth define the following combinatorial principle:Definition 1.1. Suppose κ is an infinite cardinal and n < ω. Then Hn(κ) is the statement: There is a function F: [κ]n → [[κ]ω]≤ω such that(a) ∀A ∈[κ]n ∀Y ∈ F(A)(Y ⊆ min (A)), and(b) .Hn(κ) is related to a more general principle introduced by Hajnal and Nagy in [4]. For applications of these principles to free sets for set mappings and Ramsey games we refer the reader to [3] and [4].In [3] Hajnal and Komjáth prove the consistency of ZFC + GCH + ∀n ∈ ω(Hn + 1(ωn + 1)), relative to an ω-Mahlo cardinal. They conjecture that L is a model of this theory, and suggest that the proof might require higher gap morasses. The first few cases of this conjecture are known to be true; it is easy to see that if CH holds then H1 (ω1) is true, and Laver proved that V = L implies H2(ω2). In this paper we go one step further and prove V = L → H3(ω3). Unfortunately our methods do not appear to give Hn (ωn) for n ≥ 4.Most of our notation is standard. If X is any set and κ is a cardinal number then [X]κ is the set of subsets of X with cardinality κ, and [X]≤κ is the set of subsets of X with cardinality ≤ κ. If X is a set of ordinals then tp(X) is the order type of X.

On the sets of fixed points of bounded Baire one functions

2019 ◽  
Vol 12 (03) ◽  
pp. 1950040 ◽  
Author(s):  
Aliasghar Alikhani-Koopaei
Keyword(s):  
Fixed Points ◽  
Borel Measure ◽  
Unit Interval ◽  
Baire One ◽  
Nowhere Dense Set ◽  
Class Of Functions ◽  
Dense Set ◽  
Uniformly Closed

In this paper, we present some results on typical properties of the sets of fixed points of bounded Baire one functions. In particular, we show that typical elements of a uniformly closed subclass [Formula: see text] of such class of functions have nowhere dense set of fixed points. We also show that typical elements of the class of bounded Baire one functions have [Formula: see text], where [Formula: see text] is an arbitrary continuous Borel measure on the unit interval.

Free sets for set-mappings relative to a family of sets

2017 ◽  
Vol 63 (6) ◽  
pp. 605-613
Author(s):  
Antonio Avilés ◽  
Claribet Piña
Keyword(s):  
Set Mappings ◽  
Free Sets

On a Nowhere-Dense Set

1953 ◽  
Vol 60 (6) ◽  
pp. 411
Author(s):  
Albert Wilansky
Keyword(s):  
Nowhere Dense Set ◽  
Dense Set

scholarly journals Covering a Polish group by translates of a nowhere dense set

2008 ◽  
Vol 155 (11) ◽  
pp. 1221-1226 ◽  
Author(s):  
Tadeusz Dobrowolski ◽  
Witold Marciszewski
Keyword(s):  
Polish Group ◽  
Nowhere Dense Set ◽  
Dense Set
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