10 citations · 123 across the 78 of their papers we have counts for
6 papers · 1 filter
Ultrafilter convergence in ordered topological spaces
Paolo Lipparini
We characterize ultrafilter convergence and ultrafilter compactness in linearly ordered and generalized ordered topological spaces. In such spaces, and for every ultrafilter , t…
Initial λ-compactness in linearly ordered spaces
Paolo Lipparini
We show that a linearly ordered topological space is initially λ-compact if and only if it is λ-bounded, that is, every set of cardinality has compact closure. As a conseq…
On a theorem by Juhász and Szentmiklóssy
Paolo Lipparini
We extend a theorem by Juhász and Szentmiklóssy to notions related to pseudocompactness. We also allow the case when one of the cardinals under consideration is singular. We give a…
Compactness of for singular
Paolo Lipparini
We characterize the compactness properties of the product of λ copies of the space ω with the discrete topology, dealing in particular with the case λ singular, using regular and u…
Compactness of powers of ω
Paolo Lipparini
We characterize exactly the compactness properties of the product of κ copies of the space ω with the discrete topology. The characterization involves uniform ultrafilters, infinit…
Products of sequentially compact spaces and compactness with respect to a set of filters
Paolo Lipparini
We show that, under suitably general formulations, covering properties, accumulation properties and filter convergence are all equivalent notions. This general correspondence is ex…