Search results for "Normal space"
showing 3 items of 3 documents
Cardinal invariants of cellular Lindelof spaces
2018
A space X is said to be cellular-Lindelof if for every cellular family $$\mathcal {U}$$ there is a Lindelof subspace L of X which meets every element of $$\mathcal {U}$$ . Cellular-Lindelof spaces generalize both Lindelof spaces and spaces with the countable chain condition. Solving questions of Xuan and Song, we prove that every cellular-Lindelof monotonically normal space is Lindelof and that every cellular-Lindelof space with a regular $$G_\delta $$ -diagonal has cardinality at most $$2^\mathfrak {c}$$ . We also prove that every normal cellular-Lindelof first-countable space has cardinality at most continuum under $$2^{<\mathfrak {c}}=\mathfrak {c}$$ and that every normal cellular-Lindel…
On product of p-sequential spaces
2016
Abstract The product of finitely many regular p-compact p-sequential spaces is p-compact p-sequential for any free ultrafilter p as it follows from [5] . In the paper is produced an example of a Hausdorff p-compact p-sequential space whose square is not p-sequential. It is also given an example of a space which is sP-radial, wP-radial, vwP-radial for any P ⊂ μ ( τ ) but its square is neither sP-radial nor wP-radial nor vwP-radial space.
Weakly controlled Moran constructions and iterated functions systems in metric spaces
2011
We study the Hausdorff measures of limit sets of weakly controlled Moran constructions in metric spaces. The separation of the construction pieces is closely related to the Hausdorff measure of the corresponding limit set. In particular, we investigate different separation conditions for semiconformal iterated function systems. Our work generalizes well known results on self-similar sets in metric spaces as well as results on controlled Moran constructions in Euclidean spaces.