Absolute countable compactness of products and topological groups
Song, Yan-Kui
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999), p. 367-372 / Harvested from Czech Digital Mathematics Library
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In this paper, we generalize Vaughan's and Bonanzinga's results on absolute countable compactness of product spaces and give an example of a separable, countably compact, topological group which is not absolutely countably compact. The example answers questions of Matveev [8, Question 1] and Vaughan [9, Question (1)].

Publié le : 1999-01-01
Classification:  54B10,  54D20,  54D55,  54H11 
@article{119093,
     author = {Yan-Kui Song},
     title = {Absolute countable compactness of products and topological groups},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {40},
     year = {1999},
     pages = {367-372},
     zbl = {0976.54021},
     mrnumber = {1732658},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119093}
}

Song, Yan-Kui. Absolute countable compactness of products and topological groups. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) pp. 367-372. http://gdmltest.u-ga.fr/item/119093/

Arhangel'Skii A.V. On bicompacta hereditarily satisfying Suslin's condition tightness and free sequences, Soviet Math. Dokl. 12 (1971), 1253-1257. (1971) | MR 0119188

Bonanzinga M. On the product of a compact space with an hereditarily absolutely countably compact space, Comment. Math. Univ. Carolinae 38 (1997), 557-562. (1997) | MR 1485076 | Zbl 0937.54013

Van Douwen E.K. The Integer and Topology, Handbook of Set-theoertic Topology K. Kunen and J.E. Vaughan North-Holland Amsterdam (1984), 111-167. (1984) | MR 0776619

Engelking R. General Topology, Revised and completed edition, Heldermann Verlag Berlin (1989). (1989) | MR 1039321

Fleishman W.M. A new extension of countable compactness, Fund. Math. 67 (1970), 1-9. (1970) | MR 0264608

Kombarov A.P. On the product of normal spaces, Soviet. Math. Dokl. 13 (4) (1972), 1068-1071. (1972) | Zbl 0259.54006

Matveev M.V. Absolutely countably compact spaces, Topology Appl. 58 (1994), 81-92. (1994) | MR 1280711 | Zbl 0801.54021

Matveev M.V. A countably compact topological group which is not absolutely countably compact, Questions Answers Gen. Topology 11 (1993), 173-176. (1993) | MR 1234212 | Zbl 0808.54025

Stephenson R.M., Jr. Initially $\kappa$-Compact and Related Space, Handbook of Set-theoertic Topology K. Kunen and J.E. Vaughan North-Holland Amsterdam (1984), 603-632. (1984) | MR 0776632

Vaughan J.E. A countably compact, separable space which is not absolutely countably compact, Comment. Math. Univ. Carolinae 34 (1995), 197-200. (1995) | MR 1334426 | Zbl 0833.54012

Vaughan J.E. On the product of a compact space with an absolutely countably compact space, Annals of New York Acad. Soc. 788 (1996), 203-208. (1996) | MR 1460834 | Zbl 0917.54023

Vaughan J.E. Countably Compact and Sequentially Compact Spaces, Handbook of Set-theoertic Topology K. Kunen and J.E. Vaughan North-Holland Amsterdam (1984), 569-602. (1984) | MR 0776631 | Zbl 0562.54031