Displaying similar documents to “Pairwise monotonically normal spaces”

Quasi-sums in several variables.

Maksa, Gyula, Nizsalóczki, Enikő (2006)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

Similarity:

Ordered spaces with special bases

Harold Bennett, David Lutzer (1998)

Fundamenta Mathematicae

Similarity:

We study the roles played by four special types of bases (weakly uniform bases, ω-in-ω bases, open-in-finite bases, and sharp bases) in the classes of linearly ordered and generalized ordered spaces. For example, we show that a generalized ordered space has a weakly uniform base if and only if it is quasi-developable and has a G δ -diagonal, that a linearly ordered space has a point-countable base if and only if it is first-countable and has an ω-in-ω base, and that metrizability in a generalized...

Selections that characterize topological completeness

Jan van Mill, Jan Pelant, Roman Pol (1996)

Fundamenta Mathematicae

Similarity:

We show that the assertions of some fundamental selection theorems for lower-semicontinuous maps with completely metrizable range and metrizable domain actually characterize topological completeness of the target space. We also show that certain natural restrictions on the class of the domains change this situation. The results provide in particular answers to questions asked by Engelking, Heath and Michael [3] and Gutev, Nedev, Pelant and Valov [5].

Near metric properties of function spaces

P. Gartside, E. Reznichenko (2000)

Fundamenta Mathematicae

Similarity:

"Near metric" properties of the space of continuous real-valued functions on a space X with the compact-open topology or with the topology of pointwise convergence are examined. In particular, it is investigated when these spaces are stratifiable or cometrisable.

Monotone σ-complete groups with unbounded refinement

Friedrich Wehrung (1996)

Fundamenta Mathematicae

Similarity:

The real line ℝ may be characterized as the unique non-atomic directed partially ordered abelian group which is monotone σ-complete (countable increasing bounded sequences have suprema), has the countable refinement property (countable sums ∑ m a m = ∑ n b n of positive (possibly infinite) elements have common refinements) and is linearly ordered. We prove here that the latter condition is not redundant, thus solving an old problem by A. Tarski, by proving that there are many spaces (in particular,...

Borel extensions of Baire measures

J. Aldaz (1997)

Fundamenta Mathematicae

Similarity:

We show that in a countably metacompact space, if a Baire measure admits a Borel extension, then it admits a regular Borel extension. We also prove that under the special axiom ♣ there is a Dowker space which is quasi-Mařík but not Mařík, answering a question of H. Ohta and K. Tamano, and under P(c), that there is a Mařík Dowker space, answering a question of W. Adamski. We answer further questions of H. Ohta and K. Tamano by showing that the union of a Mařík space and a compact space...

Large families of dense pseudocompact subgroups of compact groups

Gerald Itzkowitz, Dmitri Shakhmatov (1995)

Fundamenta Mathematicae

Similarity:

We prove that every nonmetrizable compact connected Abelian group G has a family H of size |G|, the maximal size possible, consisting of proper dense pseudocompact subgroups of G such that H ∩ H'={0} for distinct H,H' ∈ H. An easy example shows that connectedness of G is essential in the above result. In the general case we establish that every nonmetrizable compact Abelian group G has a family H of size |G| consisting of proper dense pseudocompact subgroups of G such that each intersection...

ℳ-rank and meager groups

Ludomir Newelski (1996)

Fundamenta Mathematicae

Similarity:

Assume p* is a meager type in a superstable theory T. We investigate definability properties of p*-closure. We prove that if T has < 2 ℵ 0 countable models then the multiplicity rank ℳ of every type p is finite. We improve Saffe’s conjecture.

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.