# Countable Toronto spaces

Fundamenta Mathematicae (2000)

- Volume: 163, Issue: 2, page 143-162
- ISSN: 0016-2736

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topGruenhage, Gary, and Moore, J.. "Countable Toronto spaces." Fundamenta Mathematicae 163.2 (2000): 143-162. <http://eudml.org/doc/212435>.

@article{Gruenhage2000,

abstract = {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 $α < ω_1$.},

author = {Gruenhage, Gary, Moore, J.},

journal = {Fundamenta Mathematicae},

language = {eng},

number = {2},

pages = {143-162},

title = {Countable Toronto spaces},

url = {http://eudml.org/doc/212435},

volume = {163},

year = {2000},

}

TY - JOUR

AU - Gruenhage, Gary

AU - Moore, J.

TI - Countable Toronto spaces

JO - Fundamenta Mathematicae

PY - 2000

VL - 163

IS - 2

SP - 143

EP - 162

AB - 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 $α < ω_1$.

LA - eng

UR - http://eudml.org/doc/212435

ER -

## References

top- [F] Z. Frolík, Fixed point maps of βN, Bull. Amer. Math. Soc. 74 (1968), 187-191. Zbl0206.51902
- [Ka] M. Katětov, On idempotent filters, Časopis Pěst. Mat. 102 (1977), 412-418. Zbl0375.54007
- [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.

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