Filters, consonance and hereditary Baireness

✍ Scribed by A. Bouziad

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 128 KB
• Volume: 104
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(99)00014-0

✦ Synopsis

A topological space is called consonant if, on the set of all closed subsets of X, the co-compact topology coincides with the upper Kuratowski topology. For a filter F on the set of natural numbers ω, let X F = ω ∪ {∞} be the space for which all points in ω are isolated and the neighborhood system of ∞ is {A ∪ {∞}: A ∈ F}. We give a combinatorial characterization of the class Φ of all filters F such that the space X F is consonant and all its compact subsets are finite. It is also shown that a filter F belongs to Φ if and only if the space C p (X F ) of real-valued continuous functions on X F with the pointwise topology is hereditarily Baire.