Baire spaces and graph theorems
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- by Dominik Noll PDF
- Proc. Amer. Math. Soc. 96 (1986), 141-151 Request permission
Abstract:
We prove graph theorems and a variant of the Banach-Steinhaus theorem in a purely topological context. We obtain characterizations of Baire spaces in the class of metrizable spaces by means of graph theorems.References
- J. C. Bradford and Casper Goffman, Metric spaces in which Blumberg’s theorem holds, Proc. Amer. Math. Soc. 11 (1960), 667–670. MR 146310, DOI 10.1090/S0002-9939-1960-0146310-1
- T. Byczkowski and R. Pol, On the closed graph and open mapping theorems, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), no. 9, 723–726 (English, with Russian summary). MR 423286
- J. Chaber, M. M. Čoban, and K. Nagami, On monotonic generalizations of Moore spaces, Čech complete spaces and $p$-spaces, Fund. Math. 84 (1974), no. 2, 107–119. MR 343244, DOI 10.4064/fm-84-2-107-119
- Jack G. Ceder, Some generalizations of metric spaces, Pacific J. Math. 11 (1961), 105–125. MR 131860
- Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna, Tom 47. [Mathematics Library. Vol. 47]. MR 0500779
- Taqdir Husain, Introduction to topological groups, W. B. Saunders Co., Philadelphia, Pa.-London, 1966. MR 0200383
- Thomas J. Jech, Lectures in set theory, with particular emphasis on the method of forcing, Lecture Notes in Mathematics, Vol. 217, Springer-Verlag, Berlin-New York, 1971. MR 0321738
- John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
- Gottfried Köthe, Topological vector spaces. II, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 237, Springer-Verlag, New York-Berlin, 1979. MR 551623
- K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751
- Kazimierz Kuratowski and Andrzej Mostowski, Teoria mnogości, Third revised edition, Monografie Matematyczne [Mathematical Monographs], vol. 27, Państwowe Wydawnictwo Naukowe (PWN), Warsaw, 1978 (Polish). With an introduction to descriptive set theory. MR 514701 V. L. Levin and D. A. Raĭkow, Closed graph theorems for uniform spaces, Soviet Math. Dokl. 4 (1963), 791 ff.
- John C. Oxtoby, The Banach-Mazur game and Banach category theorem, Contributions to the theory of games, vol. 3, Annals of Mathematics Studies, no. 39, Princeton University Press, Princeton, N.J., 1957, pp. 159–163. MR 0093741
- J. D. Weston, On the comparison of topologies, J. London Math. Soc. 32 (1957), 342–354. MR 94776, DOI 10.1112/jlms/s1-32.3.342
- H. E. White Jr., Topological spaces that are $\alpha$-favorable for a player with perfect information, Proc. Amer. Math. Soc. 50 (1975), 477–482. MR 367941, DOI 10.1090/S0002-9939-1975-0367941-0
- M. Wilhelm, Almost lower semicontinuous multifunctions and the Souslin-graph theorem, Comment. Math. Univ. Carolin. 23 (1982), no. 1, 147–158. MR 653358
- H. H. Wicke and J. M. Worrell Jr., On the open continuous images of paracompact Čech complete spaces, Pacific J. Math. 37 (1971), 265–275. MR 307173
- J. M. Worrell Jr. and H. H. Wicke, Characterizations of developable topological spaces, Canadian J. Math. 17 (1965), 820–830. MR 182945, DOI 10.4153/CJM-1965-080-3
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 141-151
- MSC: Primary 54E25; Secondary 46A30, 54C10
- DOI: https://doi.org/10.1090/S0002-9939-1986-0813827-1
- MathSciNet review: 813827