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Constructions and applications of rigid spaces. I. (English) Zbl 0403.54030


MSC:

54F99 Special properties of topological spaces
54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
03E55 Large cardinals
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[1] Arhangel’skii, A. B.; Franklin, S. P., Ordinal invariants on topological space, Michigan Math. J., 15, 313-320 (1968) · Zbl 0167.51102
[2] Berney, E. S., A chaotic space, Notices Amer. Math. Soc., 18 (1971), 71T-G6
[3] Franklin, S. P.; Rajagopalan, M., Some examples in topology, Trans. Amer. Math. Soc., 155, 305-313 (1971) · Zbl 0217.48104
[4] Freyd, P., Abelian Categories (1964), New York · Zbl 0121.02103
[5] Gillman, L.; Jerison, M., Rings of Continuous Functions (1975), Springer-Verlag: Springer-Verlag New York/Berlin · Zbl 0151.30003
[6] De Groot, J., Groups represented by homeomorphism groups, I, Math. Ann., 138, 80-102 (1959) · Zbl 0087.37802
[7] De Groot, J.; McDowell, R. H., Auto-homeomorphism groups of 0-dimensional space, Compositio Math., 15, 203-209 (1963) · Zbl 0115.40203
[8] De Groot, J.; Maurice, M. A., On the existence of rigid compact ordered spaces, (Proc. Amer. Math. Soc., 19 (1968)), 844-846 · Zbl 0162.32304
[9] Herrlich, H., Topological coreflections, (Proceedings of the International Symposium on Topology and Its Applications. Proceedings of the International Symposium on Topology and Its Applications, Herceg-Novi, Yugoslavia (1968)) · Zbl 0204.22403
[10] Herrlich, H., Topologischer Reflectionen und Co-reflectionen, (Lecture Notes in Mathematics, Vol. 78 (1968), Springer-Verlag: Springer-Verlag Berlin/New York)
[11] Herrlich, H., On the concept of reflections in general topology, (Proceedings of the International Symposium on the Extension Theory of Topological Structures and Its Applications. Proceedings of the International Symposium on the Extension Theory of Topological Structures and Its Applications, Berlin, 1967 (1968)), 105-114
[12] Herrlich, H., Separation axioms and direct limits, Canad. Math. Bull., 12, 337-338 (1969) · Zbl 0179.51103
[13] Herrlich, H., Categorical topology, Gen. Topology Appl., 1, 1-15 (1971) · Zbl 0215.51501
[14] Herrlich, H., An example in category theory, Math. Z., 113, 309-312 (1970) · Zbl 0179.32102
[15] Herrlich, H.; Strecker, G. E., Coreflective subcategories, Trans. Amer. Math. Soc., 157, 205-226 (1971) · Zbl 0224.18003
[16] Hewitt, E., On two problems of Urysohn, Ann. of Math., 47, 503-509 (1946) · Zbl 0060.39511
[17] Henricksen, M.; Isbell, J. R., Averages of continuous functions, Bull. Amer. Math. Soc., 90, 287-290 (1964) · Zbl 0119.10102
[18] Kannan, V., Ordinal invariants in topology, I: Gen. Topol. and its Applications, 5, 269-297 (1975)
[19] Kannan, V., Notes on Homogeneous Spaces, Technical Report of Madurai University (1972)
[20] Kannan, V.; Rajagopalan, M., On rigidity and groups of homeomorphisms, (Proceedings of the Third Prague Topological Symposium. Proceedings of the Third Prague Topological Symposium, 1971 (1973)), 231-234 · Zbl 0311.54042
[21] Kannan, V.; Rajagopalan, M., Constructions and Applications of Rigid Spaces III, Canada J. Math. (1978), to appear · Zbl 0424.54029
[22] V. Kannan and M. Rajagopalan; V. Kannan and M. Rajagopalan · Zbl 0641.54022
[23] Kannan, V.; Rajagopalan, M., Constructions and applications of rigid spaces, II, Amer. J. Math. (1978), to appear · Zbl 0424.54028
[24] Katetov, M., Remarks on Boolean algebras, Colloq. Math., 2, 229-235 (1951) · Zbl 0045.00903
[25] Kennison, J. F., Reflective functors in general topology and elsewhere, Trans. Amer. Math. Soc., 188, 303-315 (1965) · Zbl 0134.40705
[26] Lozier, F. W., A class of compact rigid 0-dimensional spaces, Canad. J. Math., 21, 817-821 (1969) · Zbl 0191.53403
[27] Martin, J., Homogeneous countable connected Hausdorff spaces, (Proc. Amer. Math. Soc., 12 (1961)), 308-314 · Zbl 0123.39402
[28] Mitchell, B., Theory of Categories (1965), Academic Press: Academic Press New York
[29] Nix, E. D., Chaotic spaces, Bull. Amer. Math. Soc., 76, 975 (1970)
[30] Raikhberg, A. I., Extremally unconnected spaces with unique auto-homeomorphism, (Dokl. Akad. Nauk. SSSR, 195 (1970))
[31] Rieger, L., Some remarks on automorphisms of Boolean algebras, Fund. Math., 38, 209-216 (1951) · Zbl 0044.26102
[32] Roy, P., A countable connected Urysohn space with a dispersion point, Duke Math. J., 33 (1966) · Zbl 0147.22804
[33] Sierpinski, W., Introduction to General Topology (1934), Univ. of Toronto Press: Univ. of Toronto Press Toronto · JFM 60.0502.01
[34] Shimrat, M., Embedding in homogeneous spaces, Quart. J. Math. Oxford Ser., 5, 304-311 (1954) · Zbl 0056.41601
[35] Sirota, S., Homogeneous subsets of absolutes, Soviet. Math. Dokl., 10, 1494-1497 (1969) · Zbl 0198.27302
[36] Skula, L., On a reflective subcategory of the category of topological spaces, Trans. Amer. Math. Soc., 142, 37-41 (1969) · Zbl 0185.50401
[37] Urysohn, P., Uber die Michtigkeit der Zusamman-hengenden Mengen, Math. Ann., 94, 212-295 (1925)
[38] Vaidyanathaswamy, R., Set Topology (1960), Chelsea: Chelsea New York · Zbl 0923.54001
[39] Trnkova, V., Non-constant continuous mappings of metric or compact Hausdorff spaces, Comment Math. Univ. Carolinae, 13, 283-295 (1972) · Zbl 0245.54040
[40] J. R. Isbell; J. R. Isbell
[41] Comfort, W. W.; Negropontis, S., The theory of ultrafilters (1974), Springer-Verlag: Springer-Verlag Berlin · Zbl 0298.02004
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