A countably compact, separable space which is not absolutely countably compact
Vaughan, Jerry E.
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995), p. 197-201 / Harvested from Czech Digital Mathematics Library

We construct a space having the properties in the title, and with the same technique, a countably compact $T_2$ topological group which is not absolutely countably compact.

Publié le : 1995-01-01
Classification:  22A05,  54B10,  54D20,  54G20,  54H11
@article{118744,
     author = {Jerry E. Vaughan},
     title = {A countably compact, separable space which is not absolutely countably compact},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {36},
     year = {1995},
     pages = {197-201},
     zbl = {0833.54012},
     mrnumber = {1334426},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118744}
}
Vaughan, Jerry E. A countably compact, separable space which is not absolutely countably compact. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) pp. 197-201. http://gdmltest.u-ga.fr/item/118744/

Van Douwen E.K. The integers and topology, in Handbook of Set-Theoretic Topology, K. Kunen and J. Vaughan, eds., North-Holland, Amsterdam, 1984. | MR 0776622 | Zbl 0561.54004

Van Douwen E.K.; Reed G.M.; Roscoe A.W.; Tree I.J. Star covering properties, Topology and Appl. 39 (1991), 71-103. (1991) | MR 1103993 | Zbl 0743.54007

Engelking R. General Topology, PWN-Polish Scientific Publications, Warszawa, 1977. | MR 0500780 | Zbl 0684.54001

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

Matveev M.V. Absolutely countably compact spaces, Topology and 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 and Answers in General Topology 11 (1993), 173-176. (1993) | MR 1234212 | Zbl 0808.54025

Noble N. The continuity of functions on Cartesian products, Trans. Amer. Math. Soc. 149 (1970), 187-198. (1970) | MR 0257987 | Zbl 0229.54028

Nyikos P.J.; Vaughan J.E. Sequentially compact, Franklin-Rajagopalan spaces, Proc. Amer. Math. Soc. 101 (1987), 149-155. (1987) | MR 0897087 | Zbl 0626.54004

Scarborough C.T.; Stone A.H. Products of nearly compact spaces, Trans. Amer. Math. Soc. 124 (1966), 131-147. (1966) | MR 0203679 | Zbl 0151.30001

Vaughan J.E. Countably compact and sequentially compact spaces, in Handbook of Set- theoretic Topology, eds. K. Kunen and J. Vaughan, North-Holland, Amsterdam, 1984. | MR 0776631 | Zbl 0562.54031

Vaughan J.E. Small uncountable cardinals in topology, in Problems in Topology, eds. Jan van Mill and M.G. Reed, North-Holland, Amsterdam, 1990. | MR 1078647

Vaughan J.E. A countably compact, separable space which is not absolutely countably compact. Preliminary Report, Abstracts Amer. Math. Soc. 14 (November 1993), No. 888-54-37.