Exponential density vs exponential domination

• Published in: Acta mathematica Hungarica 2021-06, Vol.164 (1), p.232-242
• Main Authors: Bella, A., Tkachuk, V. V.
• Format: Article
• Language: English
• Subjects: Density; Mathematics; Mathematics and Statistics; Subspaces
• ISSN: 0236-5294; 1588-2632
• DOI: 10.1007/s10474-021-01130-0

It is established that a space X with exponential κ -domination has density not exceeding κ if l ( X ) ≤ κ and t ( X ) ≤ κ . We also introduce a weaker property called exponential κ - density and show that it behaves nicely under standard operations. It is proved that exponential κ -density is preserved by continuous images, open subspaces, arbitrary products and extensions. Just like exponential κ -domination, exponential κ -density of X implies that κ + is a caliber of X ; every dyadic compact space must have exponential ø -density while spaces with exponential κ -density and π -character not exceeding 2 κ have density ≤ κ . In monotonically normal spaces, exponential κ -density coincides with density ≤ κ while under the hypothesis 2 κ = κ + , it follows from s ( X ) ≤ κ that d ( X ) ≤ κ whenever X is a space with exponential κ -density.