Embedding compact spaces into compact spaces with few regular open Baire subsets

Domain representations of spaces of compact subsets

On Weakly Compact Subsets of Banach Spaces

Introduction. The two sections of this note are independent, but they are related by the fact that both use the results of [5 ] to obtain information on the properties of weakly compact sets in Banach spaces. In the first section we prove some results on a class of compact sets which is believed to include all weakly compact subsets of Banach spaces. We are interested in the properties of the n...

Compact Subsets of Spaces of Holomorphic Functions

In [1] compactness criteria in function spaces are investigated for general coorbit spaces. As an application it is shown that a bounded and closed subset A ⊂ F := {f : f is entire and Z C |f(z)|2e−|z| dλ(z) < ∞} is compact if and only if ∀2 > 0 ∃ a compact subset C ⊂ Cn with Z CC |f(z)|2e−|z| dλ(z) < 2 ∀f ∈ A. The methods of [1] cannot be easily adopted for the spaces Fm := {f : f is entire an...

Compact subsets of the Baire space

Let P be the natural forcing for producing a finite splitting tree using finite conditions. Namely, p ∈ P iff p ⊆ ω is a finite subtree and p ≤ q iff p ⊇ q is an end extension of q. End extension means if s ∈ p\q then s ⊇ t for some t ∈ q which is terminal in q, i.e., has no extensions in q. This order is countable and hence forcing equivalent to adding a single Cohen real. The union of P-gener...

Compact Subsets of the First Baire Class

Perhaps the earliest results about pointwise compact sets of Baire class-1 functions are the two selection theorems of E. Helly found in most of the standard texts on real variable (see, e.g., [Lo], [N]). These two theorems are really theorems about a particular example of a compact set of Baire class-1 functions known today as Helly space, the space of all nondecreasing functions from the unit...