On finite powers of countably compact groups
Tomita, Artur Hideyuki
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996), p. 617-626 / Harvested from Czech Digital Mathematics Library
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We will show that under ${M\kern -1.8pt A\kern 0.2pt }_{countable}$ for each $k \in \Bbb N$ 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 $k \in \Bbb N$ 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.

Publié le : 1996-01-01
Classification:  22A05,  54A35,  54B10,  54D20,  54H11 
@article{118868,
     author = {Artur Hideyuki Tomita},
     title = {On finite powers of countably compact groups},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {37},
     year = {1996},
     pages = {617-626},
     zbl = {0881.54022},
     mrnumber = {1426926},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118868}
}

Tomita, Artur Hideyuki. On finite powers of countably compact groups. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) pp. 617-626. http://gdmltest.u-ga.fr/item/118868/

Comfort W.W. Topological Groups, Handbook of Set-Theoretic Topology (K. Kunen and J. Vaughan, eds.), North-Holland, 1984, pp. 1143-1263. | MR 0776643 | Zbl 1071.54019

Comfort W.W. Problems on topological groups and other homogeneous spaces, Open Problems in Topology (J. van Mill and G. M. Reed, eds.), North-Holland, 1990, pp. 311-347. | MR 1078657

Comfort W.W.; Hofmann K.H.; Remus D. Topological groups and semigroups, Recent Progress in General Topology (M. Hušek and J. van Mill, eds.), Elsevier Science Publishers, 1992, pp. 57-144. | MR 1229123 | Zbl 0798.22001

Comfort W.W.; Ross K.A. Pseudocompactness and uniform continuity in topological groups, Pacific J. Math. 16.3 (1966), 483-496. (1966) | MR 0207886 | Zbl 0214.28502

Van Douwen E.K. The product of two countably compact topological groups, Trans. Amer. Math. Soc. 262 (Dec. 1980), 417-427. (Dec. 1980) | MR 0586725 | Zbl 0453.54006

Hajnal A.; Juhász I. A separable normal topological group need not be Lindelöf, Gen. Top. and its Appl. 6 (1976), 199-205. (1976) | MR 0431086

Hart K.P.; Van Mill J. A countably compact $H$ such that $H\times H$ is not countably compact, Trans. Amer. Math. Soc. 323 (Feb. 1991), 811-821. (Feb. 1991) | MR 0982236

Tkachenko M.G. Countably compact and pseudocompact topologies on free abelian groups, Izvestia VUZ. Matematika 34 (1990), 68-75. (1990) | MR 1083312 | Zbl 0714.22001

Tomita A.H. Between countable and sequential compactness in free abelian group, preprint.

Tomita A.H. A group under $MA_{countable}$ whose square is countably compact but whose cube is not, preprint.

Tomita A.H. The Wallace Problem: a counterexample from $M A_{countable}$ and $p$-compactness, to appear in Canadian Math. Bulletin.

Weiss W. Versions of Martin's Axiom, Handbook of Set-Theoretic Topology (K. Kunen and J. Vaughan, eds.), North-Holland, 1984, pp. 827-886. | MR 0776638 | Zbl 0571.54005