Cardinal Functions on Pixley-Roy Hyperspaces

The Topology of Systems of Hyperspaces Determined by Dimension Functions

Given a non-degenerate Peano continuum X, a dimension function D : 2∗ → [0,∞] defined on the family 2 X ∗ of compact subsets of X, and a subset Γ ⊂ [0,∞), we recognize the topological structure of the system 〈2 ,D≤γ(X)〉α∈Γ, where 2 X is the hyperspace of non-empty compact subsets of X and D≤γ(X) is the subspace of 2 X , consisting of non-empty compact subsets K ⊂ X with D(K) ≤ γ.

Induced Dynamics on the Hyperspaces

In this paper, we study the dynamics induced by finite commutative relation. We prove that the dynamics generated by such a non-trivial collection cannot be transitive/super-transitive and hence cannot exhibit higher degrees of mixing. As a consequence we establish that the dynamics induced by such a collection on the hyperspace endowedwith any admissible hit andmiss topology cannot be transiti...

Three Cardinal Functions Similar to Net Weight

The purpose of this paper is to introduce and investigate cardinal functions called pseudonet weight, weak net weight, and weak pseudonet weight. These are similar to but generally smaller than net weight. We look at how these cardinal functions relate to hereditary Lindelöf degree, hereditary density, and spread, and we study their behavior under products. An important and useful cardinal func...

Local cardinal functions of H-closed spaces

The cardinal functions of pseudocharacter, closed pseudocharacter, and character are used to examine H-closed spaces and to contrast the differences between Hclosed and minimal Hausdorff spaces. An H-closed space X is produced with the properties that |X| > 22 ψ(X) and ψ(X) > 2ψ(X).

Are social welfare functions ordinal or cardinal ?