# On finite powers of countably compact groups

Commentationes Mathematicae Universitatis Carolinae (1996)

- Volume: 37, Issue: 3, page 617-626
- ISSN: 0010-2628

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topTomita, Artur Hideyuki. "On finite powers of countably compact groups." Commentationes Mathematicae Universitatis Carolinae 37.3 (1996): 617-626. <http://eudml.org/doc/247889>.

@article{Tomita1996,

abstract = {We will show that under $\{M\hspace\{-1.8pt\}A\hspace\{0.2pt\}\}_\{countable\}$ for each $k \in \mathbb \{N\}$ there exists a group whose $k$-th power is countably compact but whose $2^k$-th power is not countably compact. In particular, for each $k \in \mathbb \{N\}$ there exists $l \in [k,2^k)$ and a group whose $l$-th power is countably compact but the $l+1$-st power is not countably compact.},

author = {Tomita, Artur Hideyuki},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {countable compactness; $\{M\hspace\{-1.8pt\}A\hspace\{0.2pt\}\}_\{countable\}$; topological groups; finite powers; countable compactness; MA; finite powers of topological groups},

language = {eng},

number = {3},

pages = {617-626},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {On finite powers of countably compact groups},

url = {http://eudml.org/doc/247889},

volume = {37},

year = {1996},

}

TY - JOUR

AU - Tomita, Artur Hideyuki

TI - On finite powers of countably compact groups

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1996

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 37

IS - 3

SP - 617

EP - 626

AB - We will show that under ${M\hspace{-1.8pt}A\hspace{0.2pt}}_{countable}$ for each $k \in \mathbb {N}$ there exists a group whose $k$-th power is countably compact but whose $2^k$-th power is not countably compact. In particular, for each $k \in \mathbb {N}$ there exists $l \in [k,2^k)$ and a group whose $l$-th power is countably compact but the $l+1$-st power is not countably compact.

LA - eng

KW - countable compactness; ${M\hspace{-1.8pt}A\hspace{0.2pt}}_{countable}$; topological groups; finite powers; countable compactness; MA; finite powers of topological groups

UR - http://eudml.org/doc/247889

ER -

## References

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