# Two spaces homeomorphic to $Seq\left(p\right)$

Commentationes Mathematicae Universitatis Carolinae (2001)

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

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topVaughan, 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 -

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