Rocky Mountain Journal of Mathematics

Non-homeomorphic Disjoint Spaces whose Union is $\o^*$

W.W. Comfort and Akio Kato

Full-text: Open access

Article information

Source
Rocky Mountain J. Math., Volume 23, Number 2 (1993), 533-545.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1181072575

Digital Object Identifier
doi:10.1216/rmjm/1181072575

Mathematical Reviews number (MathSciNet)
MR1226187

Zentralblatt MATH identifier
0792.54004

Subjects
Primary: 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets) [See also 03Exx] {For ultrafilters, see 54D80} 54D40: Remainders
Secondary: 54D30: Compactness 04A20

Keywords
Stone-Čech remainder disjoint union Rudin-Froĺık order countably compact extra countably compact disjoint refinement lemma

Citation

Comfort, W.W.; Kato, Akio. Non-homeomorphic Disjoint Spaces whose Union is $\o^*$. Rocky Mountain J. Math. 23 (1993), no. 2, 533--545. doi:10.1216/rmjm/1181072575. https://projecteuclid.org/euclid.rmjm/1181072575


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References

  • Allen R. Bernstein, A new kind of compactness for topological spaces, Fund. Math. 66 (1970), 185-193.
  • L. Bukovský and E. Butkovičová, Ultrafilters with $\aleph_0$ predecessors in Rudin-Frolí k order, Comm. Math. Univ. Carolin. 22 (1981), 429-447.
  • W.W. Comfort and Akio Kato, Non-homeomorphic disjoint spaces whose union is $\o^*$, Abstracts Amer. Math. Soc. 11 (1990), p. 332 (Abstract).
  • W.W. Comfort, Akio Kato and Saharon Shelah, Topological partition relations of the form $\o^*\to (Y)^1_2$, Proc. Seventh (1991) Summer Conference on General Topology and Applications, in honor of Mary Ellen Rudin and Her Work, Ann. New York Acad. Sci., 1993, to appear.
  • W.W. Comfort and S. Negrepontis, The theory of ultrafilters, Grundlehren der math. Wissenschaften Band 211, Springer-Verlag, Berlin, Heidelberg and New York, 1974.
  • W.W. Comfort and Victor Saks, Countably compact groups and finest totally bounded topologies, Pacific J. Math. 49 (1973), 33-44.
  • W.W. Comfort and Charles Waiveris, Intersections of countably compact subspaces of Stone-Čech compactifications, Uspekhi Mat. Nauk 35 (1980), 67-77 (in Russian). English translation: Russian Math. Surveys 35 (1980), 79-89.
  • Zden\v ek Frolí k, Sums of ultrafilters, Bull. Amer. Math. Soc. 73 (1967), 87-91.
  • Leonard Gillman and Meyer Jerison, Rings of continuous functions, D. Van Nostrand Co., Inc., Princeton, Toronto, New York and London, 1960.
  • John Ginsburg and Victor Saks, Some applications of ultrafilters to topology, Pacific J. Math. 57 (1975), 403-418.
  • R.E. Hodel, The number of metrizable spaces, Fund. Math. 115 (1983), 127-141.
  • Akio Kato, Elementary submodels for a partition of $ \b\o\backslash\o$, submitted.
  • Kenneth Kunen, Some points in $\b\N$, Math. Proc. Cambridge Philos. Soc. 80 (1976), 385-398.
  • --------, Weak $P$-points in $N^*$, Colloquia Mathematica Societatis János Bolyai 23 (1978), 741-749.
  • Jan van Mill, Sixteen topological types in $\b\o$-$ \o$, Topol. Appl. 13 (1982), 43-57.
  • --------, An introduction to $\b\o$, in Handbook of set-theoretic topology, K. Kunen and J.E. Vaughan, ed., North-Holland Publ. Co., Amsterdam, New York, Oxford, 1984.
  • Mary Ellen Rudin, Partial orders on the types of $\b \N$, Trans. Amer. Math. Soc. 155 (1971), 353-362.
  • Charles Waiveris, Intersections of countably compact subspaces of $\b X$, Topol. Proc. 4 (1979), 177-191.