Page 1 Next

Displaying 1 – 20 of 34

Showing per page

Sequential compactness vs. countable compactness

Angelo Bella, Peter Nyikos (2010)

Colloquium Mathematicae

The general question of when a countably compact topological space is sequentially compact, or has a nontrivial convergent sequence, is studied from the viewpoint of basic cardinal invariants and small uncountable cardinals. It is shown that the small uncountable cardinal 𝔥 is both the least cardinality and the least net weight of a countably compact space that is not sequentially compact, and that it is also the least hereditary Lindelöf degree in most published models. Similar results, some definitive,...

Sequential + separable vs sequentially separable and another variation on selective separability

Angelo Bella, Maddalena Bonanzinga, Mikhail Matveev (2013)

Open Mathematics

A space X is sequentially separable if there is a countable D ⊂ X such that every point of X is the limit of a sequence of points from D. Neither “sequential + separable” nor “sequentially separable” implies the other. Some examples of this are presented and some conditions under which one of the two implies the other are discussed. A selective version of sequential separability is also considered.

Some applications of the point-open subbase game

D. Guerrero Sánchez, Vladimir Vladimirovich Tkachuk (2017)

Commentationes Mathematicae Universitatis Carolinae

Given a subbase 𝒮 of a space X , the game P O ( 𝒮 , X ) is defined for two players P and O who respectively pick, at the n -th move, a point x n X and a set U n 𝒮 such that x n U n . The game stops after the moves { x n , U n : n ø } have been made and the player P wins if n ø U n = X ; otherwise O is the winner. Since P O ( 𝒮 , X ) is an evident modification of the well-known point-open game P O ( X ) , the primary line of research is to describe the relationship between P O ( X ) and P O ( 𝒮 , X ) for a given subbase 𝒮 . It turns out that, for any subbase 𝒮 , the player P has a winning strategy...

Some conditions under which a uniform space is fine

Umberto Marconi (1993)

Commentationes Mathematicae Universitatis Carolinae

Let X be a uniform space of uniform weight μ . It is shown that if every open covering, of power at most μ , is uniform, then X is fine. Furthermore, an ω μ -metric space is fine, provided that every finite open covering is uniform.

Some non-multiplicative properties are l -invariant

Vladimir Vladimirovich Tkachuk (1997)

Commentationes Mathematicae Universitatis Carolinae

A cardinal function ϕ (or a property 𝒫 ) is called l -invariant if for any Tychonoff spaces X and Y with C p ( X ) and C p ( Y ) linearly homeomorphic we have ϕ ( X ) = ϕ ( Y ) (or the space X has 𝒫 ( X 𝒫 ) iff Y 𝒫 ). We prove that the hereditary Lindelöf number is l -invariant as well as that there are models of Z F C in which hereditary separability is l -invariant.

Currently displaying 1 – 20 of 34

Page 1 Next