Two spaces homeomorphic to S e q ( p )

Jerry E. Vaughan

Commentationes Mathematicae Universitatis Carolinae (2001)

  • Volume: 42, Issue: 1, page 209-218
  • ISSN: 0010-2628

Abstract

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We consider the spaces called S e q ( u t ) , constructed on the set S e q of all finite sequences of natural numbers using ultrafilters u t to define the topology. For such spaces, we discuss continuity, homogeneity, and rigidity. We prove that S ( u t ) is homogeneous if and only if all the ultrafilters u t have the same Rudin-Keisler type. We proved that a space of Louveau, and in certain cases, a space of Sirota, are homeomorphic to S e q ( p ) (i.e., u t = p for all t ∈ S e q ). It follows that for a Ramsey ultrafilter p , S e q ( p ) is a topological group.

How to cite

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Vaughan, Jerry E.. "Two spaces homeomorphic to $Seq(p)$." Commentationes Mathematicae Universitatis Carolinae 42.1 (2001): 209-218. <http://eudml.org/doc/248763>.

@article{Vaughan2001,
abstract = {We consider the spaces called $Seq(u_t)$, constructed on the set $Seq$ of all finite sequences of natural numbers using ultrafilters $u_t$ to define the topology. For such spaces, we discuss continuity, homogeneity, and rigidity. We prove that $S(u_t)$ is homogeneous if and only if all the ultrafilters $u_t$ have the same Rudin-Keisler type. We proved that a space of Louveau, and in certain cases, a space of Sirota, are homeomorphic to $Seq(p)$ (i.e., $u_t = p$ for all $t\in Seq$). It follows that for a Ramsey ultrafilter $p$, $Seq(p)$ is a topological group.},
author = {Vaughan, Jerry E.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {ultrafilters; continuity; homeomorphisms; homogeneous; rigid; topological group; Ramsey ultrafilters; selective ultrafilters; ultrafilters; continuity; homeomorphisms; homogeneous; rigid; topological group; Ramsey ultrafilters; selective ultrafilters},
language = {eng},
number = {1},
pages = {209-218},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Two spaces homeomorphic to $Seq(p)$},
url = {http://eudml.org/doc/248763},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Vaughan, Jerry E.
TI - Two spaces homeomorphic to $Seq(p)$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 1
SP - 209
EP - 218
AB - We consider the spaces called $Seq(u_t)$, constructed on the set $Seq$ of all finite sequences of natural numbers using ultrafilters $u_t$ to define the topology. For such spaces, we discuss continuity, homogeneity, and rigidity. We prove that $S(u_t)$ is homogeneous if and only if all the ultrafilters $u_t$ have the same Rudin-Keisler type. We proved that a space of Louveau, and in certain cases, a space of Sirota, are homeomorphic to $Seq(p)$ (i.e., $u_t = p$ for all $t\in Seq$). It follows that for a Ramsey ultrafilter $p$, $Seq(p)$ is a topological group.
LA - eng
KW - ultrafilters; continuity; homeomorphisms; homogeneous; rigid; topological group; Ramsey ultrafilters; selective ultrafilters; ultrafilters; continuity; homeomorphisms; homogeneous; rigid; topological group; Ramsey ultrafilters; selective ultrafilters
UR - http://eudml.org/doc/248763
ER -

References

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