A sufficient condition of full normality

Tomáš Kaiser

The search session has expired. Please query the service again.

Displaying similar documents to “A sufficient condition of full normality”

The Arkhangel'skiĭ–Tall problem under Martin’s Axiom

Gary Gruenhage, Piotr Koszmider (1996)

Fundamenta Mathematicae

Similarity:

We show that MA $_{σ - c e n t e r e d} (ω_{1})$ implies that normal locally compact metacompact spaces are paracompact, and that MA( $ω_{1}$ ) implies normal locally compact metalindelöf spaces are paracompact. The latter result answers a question of S. Watson. The first result implies that there is a model of set theory in which all normal locally compact metacompact spaces are paracompact, yet there is a normal locally compact metalindelöf space which is not paracompact.

$τ$ -pseudocompact mappings.

Mironova, Yu.N. (2001)

Sibirskij Matematicheskij Zhurnal

Similarity:

$ℵ_{0}$ -spaces and images of separable metric spaces.

Ge, Ying (2005)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

Similarity:

Diagonal conditions in ordered spaces

Harold Bennett, David Lutzer (1997)

Fundamenta Mathematicae

Similarity:

For a space X and a regular uncountable cardinal κ ≤ |X| we say that κ ∈ D(X) if for each $T \subset X^{2} - Δ (X)$ with |T| = κ, there is an open neighborhood W of Δ(X) such that |T - W| = κ. If $ω_{1} \in D (X)$ then we say that X has a small diagonal, and if every regular uncountable κ ≤ |X| belongs to D(X) then we say that X has an H-diagonal. In this paper we investigate the interplay between D(X) and topological properties of X in the category of generalized ordered spaces. We obtain cardinal invariant theorems and metrization...

Undetermined sets of point-open games

Janusz Pawlikowski (1994)

Fundamenta Mathematicae

Similarity:

We show that a set of reals is undetermined in Galvin's point-open game iff it is uncountable and has property C", which answers a question of Gruenhage.

The hyperspace of finite subsets of a stratifiable space

Robert Cauty, Bao-Lin Guo, Katsuro Sakai (1995)

Fundamenta Mathematicae

Similarity:

It is shown that the hyperspace of non-empty finite subsets of a space X is an ANR (an AR) for stratifiable spaces if and only if X is a 2-hyper-locally-connected (and connected) stratifiable space.

Combinatorics of open covers (III): games, Cp (X)

Marion Scheepers (1997)

Fundamenta Mathematicae

Similarity:

Some of the covering properties of spaces as defined in Parts I and II are here characterized by games. These results, applied to function spaces $C_{p} (X)$ of countable tightness, give new characterizations of countable fan tightness and countable strong fan tightness. In particular, each of these properties is characterized by a Ramseyan theorem.

Universal spaces in the theory of transfinite dimension, I

Wojciech Olszewski (1994)

Fundamenta Mathematicae

Similarity:

R. Pol has shown that for every countable ordinal α, there exists a universal space for separable metrizable spaces X with ind X = α . We prove that for every countable limit ordinal λ, there is no universal space for separable metrizable spaces X with Ind X = λ. This implies that there is no universal space for compact metrizable spaces X with Ind X = λ. We also prove that there is no universal space for compact metrizable spaces X with ind X = λ.

A factorization theorem for the transfinite kernel dimension of metrizable spaces

M. Charalambous (1998)

Fundamenta Mathematicae

Similarity:

We prove a factorization theorem for transfinite kernel dimension in the class of metrizable spaces. Our result in conjunction with Pasynkov's technique implies the existence of a universal element in the class of metrizable spaces of given weight and transfinite kernel dimension, a result known from the work of Luxemburg and Olszewski.

Normal subspaces in products of two ordinals

Nobuyuki Kemoto, Tsugunori Nogura, Kerry Smith, Yukinobu Yajima (1996)

Fundamenta Mathematicae

Similarity:

Let λ be an ordinal number. It is shown that normality, collectionwise normality and shrinking are equivalent for all subspaces of ${(λ + 1)}^{2}$ .

The Arkhangel’skiĭ–Tall problem: a consistent counterexample

Gary Gruenhage, Piotr Koszmider (1996)

Fundamenta Mathematicae

Similarity:

We construct a consistent example of a normal locally compact metacompact space which is not paracompact, answering a question of A. V. Arkhangel’skiĭ and F. Tall. An interplay between a tower in P(ω)/Fin, an almost disjoint family in ${[ω]}^{ω}$ , and a version of an (ω,1)-morass forms the core of the proof. A part of the poset which forces the counterexample can be considered a modification of a poset due to Judah and Shelah for obtaining a Q-set by a countable support iteration.

A remark on R. G. Woods' paper "The minimum uniform compactification of a metric space" (Fund. Math. 147 (1995), 39–59)

M. Charalambous (1996)

Fundamenta Mathematicae

Similarity:

A question raised in R. G. Woods' paper has a simple solution.

Coherent and strong expansions of spaces coincide

Sibe Mardešić (1998)

Fundamenta Mathematicae

Similarity:

In the existing literature there are several constructions of the strong shape category of topological spaces. In the one due to Yu. T. Lisitsa and S. Mardešić [LM1-3] an essential role is played by coherent polyhedral (ANR) expansions of spaces. Such expansions always exist, because every space admits a polyhedral resolution, resolutions are strong expansions and strong expansions are always coherent. The purpose of this paper is to prove that conversely, every coherent polyhedral (ANR)...