Countable Toronto spaces

• Autorzy: Gary Gruenhage , J. Tach Moore
• Języki publikacji: EN

Abstrakty

EN

A space X is called an α-Toronto space if X is scattered of Cantor-Bendixson rank α and is homeomorphic to each of its subspaces of the same rank. We answer a question of Steprāns by constructing a countable α-Toronto space for each α ≤ ω. We also construct consistent examples of countable α-Toronto spaces for each $α < ω_1$.

Kategorie tematyczne

• 54G15: Pathological spaces
• 54A35: Consistency and independence results
• 54G12: Scattered spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2000
• Tom: 163
• Numer: 2
• Strony: 143-162

Daty

wydano

2000

otrzymano

1999-02-12

poprawiono

1999-07-22

poprawiono

1999-09-07

Twórcy

autor

Gary Gruenhage

• Department of Mathematics, Auburn University, Auburn, AL 36849, U.S.A.

autor

J. Tach Moore

• Department of Mathematics, University of Toronto, Toronto, Ontario M5S 1A1, Canada

Bibliografia

• [F] Z. Frolík, Fixed point maps of βN, Bull. Amer. Math. Soc. 74 (1968), 187-191.
• [Ka] M. Katětov, On idempotent filters, Časopis Pěst. Mat. 102 (1977), 412-418.
• [Ku] K. Kunen, Set Theory, North-Holland, Amsterdam, 1980.
• [S] J. Steprāns, Steprāns' problems, in: Open Problems in Topology, J. van Mill and G. M. Reed (eds.), North-Holland, Amsterdam, 1990, 13-20.