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Displaying 1341 – 1360 of 1977

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Properties of one-point completions of a noncompact metrizable space

Melvin Henriksen, Ludvík Janoš, Grant R. Woods (2005)

Commentationes Mathematicae Universitatis Carolinae

If a metrizable space X is dense in a metrizable space Y , then Y is called a metric extension of X . If T 1 and T 2 are metric extensions of X and there is a continuous map of T 2 into T 1 keeping X pointwise fixed, we write T 1 ≤ T 2 . If X is noncompact and metrizable, then ( ℳ ( X ) , ≤ ) denotes the set of metric extensions of X , where T 1 and T 2 are identified if T 1 ≤ T 2 and T 2 ≤ T 1 , i.e., if there is a homeomorphism of T 1 onto T 2 keeping X pointwise fixed. ( ℳ ( X ) , ≤ ) is a large complicated poset studied extensively by V. Bel’nov [The structure of...

Properties of the class of measure separable compact spaces

Mirna Džamonja, Kenneth Kunen (1995)

Fundamenta Mathematicae

We investigate properties of the class of compact spaces on which every regular Borel measure is separable. This class will be referred to as MS. We discuss some closure properties of MS, and show that some simply defined compact spaces, such as compact ordered spaces or compact scattered spaces, are in MS. Most of the basic theory for regular measures is true just in ZFC. On the other hand, the existence of a compact ordered scattered space which carries a non-separable (non-regular) Borel measure...

Property ( a ) and dominating families

Samuel Gomes da Silva (2005)

Commentationes Mathematicae Universitatis Carolinae

Generalizations of earlier negative results on Property ( a ) are proved and two questions on an ( a ) -version of Jones’ Lemma are posed. We discuss these questions in the realm of locally compact spaces. Using dominating families of functions as a tool, we prove that under the assumptions “ 2 ω is regular” and “ 2 ω < 2 ω 1 ” the existence of a T 1 separable locally compact ( a ) -space with an uncountable closed discrete subset implies the existence of inner models with measurable cardinals. We also use cardinal invariants...

Property Q.

Bandy, C. (1991)

International Journal of Mathematics and Mathematical Sciences

P-sets and minimal right ideals in ℕ*

W. R. Brian (2015)

Fundamenta Mathematicae

Recall that a P-set is a closed set X such that the intersection of countably many neighborhoods of X is again a neighborhood of X. We show that if 𝔱 = 𝔠 then there is a minimal right ideal of (βℕ,+) that is also a P-set. We also show that the existence of such P-sets implies the existence of P-points; in particular, it is consistent with ZFC that no minimal right ideal is a P-set. As an application of these results, we prove that it is both consistent with and independent of ZFC that the shift...

Pseudocompactness and the cozero part of a frame

Bernhard Banaschewski, Christopher Gilmour (1996)

Commentationes Mathematicae Universitatis Carolinae

A characterization of the cozero elements of a frame, without reference to the reals, is given and is used to obtain a characterization of pseudocompactness also independent of the reals. Applications are made to the congruence frame of a σ -frame and to Alexandroff spaces.

Pseudouniform topologies on C ( X ) given by ideals

Roberto Pichardo-Mendoza, Angel Tamariz-Mascarúa, Humberto Villegas-Rodríguez (2013)

Commentationes Mathematicae Universitatis Carolinae

Given a Tychonoff space X , a base α for an ideal on X is called pseudouniform if any sequence of real-valued continuous functions which converges in the topology of uniform convergence on α converges uniformly to the same limit. This paper focuses on pseudouniform bases for ideals with particular emphasis on the ideal of compact subsets and the ideal of all countable subsets of the ground space.

Currently displaying 1341 – 1360 of 1977