P-sets and minimal right ideals in ℕ*

• Autorzy: W. R. Brian
• Języki publikacji: EN

Abstrakty

EN

Recall that a P-set is a closed set X such that the intersection of countably many neighborhoods of X is again a neighborhood of X. We show that if 𝔱 = 𝔠 then there is a minimal right ideal of (βℕ,+) that is also a P-set. We also show that the existence of such P-sets implies the existence of P-points; in particular, it is consistent with ZFC that no minimal right ideal is a P-set. As an application of these results, we prove that it is both consistent with and independent of ZFC that the shift map and its inverse are (up to isomorphism) the unique chain transitive autohomeomorphisms of ℕ*.

Kategorie tematyczne

• 03E17: Cardinal characteristics of the continuum
• 22A15: Structure of topological semigroups
• 37B99: None of the above, but in this section
• 03E35: Consistency and independence results
• 54D35: Extensions of spaces (compactifications, supercompactifications, completions, etc.)
• 06A07: Combinatorics of partially ordered sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 229
• Numer: 3
• Strony: 277-293

Daty

wydano

2015

Twórcy

autor

W. R. Brian

• Department of Mathematics, Tulane University, 6823 St. Charles Ave., New Orleans, LA 70118, U.S.A.

Identyfikatory

DOI

10.4064/fm229-3-4