Displaying similar documents to “Partitions of compact Hausdorff spaces”

Open subspaces of countable dense homogeneous spaces

Stephen Watson, Petr Simon (1992)

Fundamenta Mathematicae

Similarity:

We construct a completely regular space which is connected, locally connected and countable dense homogeneous but not strongly locally homogeneous. The space has an open subset which has a unique cut-point. We use the construction of a C 1 -diffeomorphism of the plane which takes one countable dense set to another.

Lindelöf property and the iterated continuous function spaces

G. Sokolov (1993)

Fundamenta Mathematicae

Similarity:

We give an example of a compact space X whose iterated continuous function spaces C p ( X ) , C p C p ( X ) , . . . are Lindelöf, but X is not a Corson compactum. This solves a problem of Gul’ko (Problem 1052 in [11]). We also provide a theorem concerning the Lindelöf property in the function spaces C p ( X ) on compact scattered spaces with the ω 1 th derived set empty, improving some earlier results of Pol [12] in this direction.

Large free set

Kandasamy Muthuvel (1992)

Colloquium Mathematicae

Similarity:

Finite union of H-sets and countable compact sets

Sylvain Kahane (1993)

Colloquium Mathematicae

Similarity:

In [2], D. E. Grow and M. Insall construct a countable compact set which is not the union of two H-sets. We make precise this result in two directions, proving such a set may be, but need not be, a finite union of H-sets. Descriptive set theory tools like Cantor-Bendixson ranks are used; they are developed in the book of A. S. Kechris and A. Louveau [6]. Two proofs are presented; the first one is elementary while the second one is more general and useful. Using the last one I prove in...

Linear subspace of Rl without dense totally disconnected subsets

K. Ciesielski (1993)

Fundamenta Mathematicae

Similarity:

In [1] the author showed that if there is a cardinal κ such that 2 κ = κ + then there exists a completely regular space without dense 0-dimensional subspaces. This was a solution of a problem of Arkhangel’skiĭ. Recently Arkhangel’skiĭ asked the author whether one can generalize this result by constructing a completely regular space without dense totally disconnected subspaces, and whether such a space can have a structure of a linear space. The purpose of this paper is to show that indeed such...

A dichotomy for P-ideals of countable sets

Stevo Todorčević (2000)

Fundamenta Mathematicae

Similarity:

A dichotomy concerning ideals of countable subsets of some set is introduced and proved compatible with the Continuum Hypothesis. The dichotomy has influence not only on the Suslin Hypothesis or the structure of Hausdorff gaps in the quotient algebra P ( ℕ ) / but also on some higher order statements like for example the existence of Jensen square sequences.

Fragmentability and σ-fragmentability

J. Jayne, I. Namioka, C. Rogers (1993)

Fundamenta Mathematicae

Similarity:

Recent work has studied the fragmentability and σ-fragmentability properties of Banach spaces. Here examples are given that justify the definitions that have been used. The fragmentability and σ-fragmentability properties of the spaces ℓ ∞ and ℓ c ∞ ( Γ ) , with Γ uncountable, are determined.

Composant-like decompositions

Wojciech Dębski, E. Tymchatyn (1991)

Fundamenta Mathematicae

Similarity:

The body of this paper falls into two independent sections. The first deals with the existence of cross-sections in F σ -decompositions. The second deals with the extensions of the results on accessibility in the plane.

Functions characterized by images of sets

Krzysztof Ciesielski, Dikran Dikrajan, Stephen Watson (1998)

Colloquium Mathematicae

Similarity:

For non-empty topological spaces X and Y and arbitrary families 𝒜 ⊆ 𝒫 ( X ) and ℬ ⊆ 𝒫 ( Y ) we put 𝒞 𝒜 , ℬ =f ∈ Y X : (∀ A ∈ 𝒜 )(f[A] ∈ ℬ ) . We examine which classes of functions ℱ ⊆ Y X can be represented as 𝒞 𝒜 , ℬ . We are mainly interested in the case when ℱ = 𝒞 ( X , Y ) is the class of all continuous functions from X into Y. We prove that for a non-discrete Tikhonov space X the class ℱ = 𝒞 (X,ℝ) is not equal to 𝒞 𝒜 , ℬ for any 𝒜 ⊆ 𝒫 ( X ) and ℬ ⊆ 𝒫 (ℝ). Thus, 𝒞 (X,ℝ) cannot be characterized by images of sets. We also show that none of the following...