Two spaces homeomorphic to $Seq(p)$
Vaughan, Jerry E.
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001), p. 209-218 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 2001-01-01
Classification:  54A35,  54C05,  54D80,  54G05,  54H11 
@article{119236,
     author = {Jerry E. Vaughan},
     title = {Two spaces homeomorphic to $Seq(p)$},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {42},
     year = {2001},
     pages = {209-218},
     zbl = {1053.54033},
     mrnumber = {1825385},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119236}
}

Vaughan, Jerry E. Two spaces homeomorphic to $Seq(p)$. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) pp. 209-218. http://gdmltest.u-ga.fr/item/119236/

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