Proper pseudocompact extensions of compact abelian group topologies
HTML articles powered by AMS MathViewer
- by W. W. Comfort and Lewis C. Robertson
- Proc. Amer. Math. Soc. 86 (1982), 173-178
- DOI: https://doi.org/10.1090/S0002-9939-1982-0663891-4
- PDF | Request permission
Abstract:
A compact Abelian group $G$ admits a strictly finer pseudocompact topological group topology if and only if the weight of $G$ is uncountable.References
- W. W. Comfort and Lewis C. Robertson, Cardinality constraints for pseudocompact and for totally dense subgroups of compact Abelian groups (in preparation).
- W. W. Comfort and K. A. Ross, Topologies induced by groups of characters, Fund. Math. 55 (1964), 283–291. MR 169940, DOI 10.4064/fm-55-3-283-291
- W. W. Comfort and Kenneth A. Ross, Pseudocompactness and uniform continuity in topological groups, Pacific J. Math. 16 (1966), 483–496. MR 207886
- W. W. Comfort and T. Soundararajan, Pseudocompact group topologies and totally dense subgroups, Pacific J. Math. 100 (1982), no. 1, 61–84. MR 661441
- Leonard Gillman and Meyer Jerison, Rings of continuous functions, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0116199
- Douglass L. Grant, Topological groups which satisfy an open mapping theorem, Pacific J. Math. 68 (1977), no. 2, 411–423. MR 466395 Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis I, Grundlehren der math. Wissenschaften, vol. 115, Springer-Verlag, Berlin and New York, 1963.
- Edwin Hewitt and Kenneth A. Ross, Extensions of Haar measure and of harmonic analysis for locally compact Abelian groups, Math. Ann. 160 (1965), 171–194. MR 186751, DOI 10.1007/BF01360918 —, Abstract harmonic analysis II, Grundlehren der math. Wissenschaften, vol. 152, Springer-Verlag, Berlin and New York, 1970.
- M. Rajagopalan, Topologies in locally compact groups, Math. Ann. 176 (1968), 169–180. MR 224736, DOI 10.1007/BF02052823
- Neil W. Rickert, Locally compact topologies for groups, Trans. Amer. Math. Soc. 126 (1967), 225–235. MR 202911, DOI 10.1090/S0002-9947-1967-0202911-4
- K. A. Ross, Closed subgroups of locally compact Abelian groups, Fund. Math. 56 (1964), 241–244. MR 171878, DOI 10.4064/fm-56-2-241-244
- T. Soundararajan, Galois theory for general extension fields, J. Reine Angew. Math. 241 (1970), 49–63. MR 262211, DOI 10.1515/crll.1970.241.49 —, Totally dense subgroups of topological groups, General Topology and Its Relations to Modern Analysis and Algebra, III, (Proc. Topological Conf., Kanpur, 1968), Academia, Prague, 1971, pp. 299-300.
- T. Soundararajan, Cohomology of Galois extensions, J. Pure Appl. Algebra 11 (1977/78), no. 1-3, 139–150. MR 466092, DOI 10.1016/0022-4049(77)90048-2 —, Pseudocompact subgroups of Galois groups (to appear).
- R. M. Stephenson Jr., Pseudocompact spaces, Trans. Amer. Math. Soc. 134 (1968), 437–448. MR 232349, DOI 10.1090/S0002-9947-1968-0232349-6
- R. M. Stephenson Jr., Minimal topological groups, Math. Ann. 192 (1971), 193–195. MR 286934, DOI 10.1007/BF02052870 André Weil, Sur les espaces à structure uniforme et sur la topologie générale, Publ. Math. Univ. Strasbourg, Hermann, Paris, 1937.
- Howard J. Wilcox, Pseudocompact groups, Pacific J. Math. 19 (1966), 365–379. MR 206139
- Howard J. Wilcox, Dense subgroups of compact groups, Proc. Amer. Math. Soc. 28 (1971), 578–580. MR 280640, DOI 10.1090/S0002-9939-1971-0280640-5
Bibliographic Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 173-178
- MSC: Primary 22B05; Secondary 22D05, 54H99
- DOI: https://doi.org/10.1090/S0002-9939-1982-0663891-4
- MathSciNet review: 663891