Sequential continuity on dyadic compacta and topological groups
Arhangel'skii, Aleksander V. ; Just, Winfried ; Plebanek, Grzegorz
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996), p. 775-790 / Harvested from Czech Digital Mathematics Library
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We study conditions under which sequentially continuous functions on topological spaces and sequentially continuous homomorphisms of topological groups are continuous.

Publié le : 1996-01-01
Classification:  03E35,  03E55,  54A25,  54A35,  54C08,  54D30,  54E45,  54H11 
@article{118884,
     author = {Aleksander V. Arhangel'skii and Winfried Just and Grzegorz Plebanek},
     title = {Sequential continuity on dyadic compacta and topological groups},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {37},
     year = {1996},
     pages = {775-790},
     zbl = {0887.54013},
     mrnumber = {1440707},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118884}
}

Arhangel'skii, Aleksander V.; Just, Winfried; Plebanek, Grzegorz. Sequential continuity on dyadic compacta and topological groups. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) pp. 775-790. http://gdmltest.u-ga.fr/item/118884/

Arhangel'Skii A.V. The frequency spectrum of a topological space and the product operation (in Russian), Trudy Mosk. Mat. Ob-va 40 (1979), 171-206; English transl.: Trans. Moscow Math. Soc. 40.2 (1981) 163-200. (1979) | MR 0550259

Arhangel'Skii A.V. On countably compact topologies on compact groups and on dyadic compacta, Top. and Appl. 57 (1994), 163-181. (1994) | MR 1278022

Arhangel'Skii A.V. On invariants of character and weight type (in Russian), Trudy Mosk. Mat. Ob-va 38 (1979), 3-23; English transl.: Trans. Moscow Math. Soc. 38.2 (1980), 1-23. (1979) | MR 0544935

Antonovskiĭm., Chudnovskiĭd. Some questions of general topology and Tichonov semifields II., Russian Math. Surveys 31 (1976), 69-128. (1976)

Booth D. A Boolean view of sequential compactness, Fund. Math. 85 (1974), 99-102. (1974) | MR 0367926 | Zbl 0297.54020

Ciesielski K. Real-valued sequentially continuous functions on the product space $2^\kappa$, unpublished preprint.

Comfort W.W.; Remus D. Compact groups of Ulam-measurable cardinality: Partial converses of theorems of Arhangel'skii and Varopoulos, Math. Japonica 39.2 (1994), 203-210. (1994) | MR 1270627

Van Douwen E.K. The integers and topology, in: Handbook of Set-theoretical Topology, K. Kunen and J.E. Vaughan eds., North Holland, 1984, pp.111-167. | MR 0776619 | Zbl 0561.54004

Engelking R. General Topology, Heldermann Verlag, Berlin, 1989. | MR 1039321 | Zbl 0684.54001

Engelking R. Cartesian products and dyadic spaces, Fund. Math. 57.3 (1965), 287-304. (1965) | MR 0196692 | Zbl 0173.50603

Engelking R.; Karłowicz M. Some theorems of set theory and their topological consequences, Fund. Math. 57.3 (1965), 275-285. (1965) | MR 0196693

Fremlin D.H. Measure algebras, in: Handbook of Boolean Algebras, J.D. Monk ed., North Holland, 1989, pp.876-980. | MR 0991611 | Zbl 1165.28002

Fremlin D.H. Real-valued-measurable cardinals, in: Set Theory of the Reals, H. Judah ed., Israel Mathematical Conference Proceedings 6 (1993) 151-304. | MR 1234282 | Zbl 0839.03038

Gryllakis C. Products of completion-regular measures, Proc. Amer. Math. Soc. 103 (1988), 563-568. (1988) | MR 0943085 | Zbl 0655.28005

Hagler J. On the structure of $S$ and $C(S)$ for $S$ dyadic, Trans. AMS 213 (1975), 415-428. (1975) | MR 0388062 | Zbl 0321.46022

Halmos P.R. Measure Theory, Van Nostrand, New York, 1950. | MR 0033869 | Zbl 0283.28001

Hušek M. Sequentially continuous homomorphisms on products of topological groups, preprint, October 1995. | MR 1397074

Jech T. Set Theory, Academic Press, 1978. | MR 0506523 | Zbl 1007.03002

Ivanovskĭl.N. On a hypothesis of P.S. Alexandroff, Dokl. AN SSSR 123.4 (1958), 785-786. (1958)

Kuz'Minov V.I. On a hypothesis of P.S. Alexandroff in the theory of topological groups, Dokl. AN SSSR 125.4 (1959), 727-729. (1959) | MR 0104753

Mazur S. On continuous mappings on Cartesian products, Fund. Math. 39 (1952), 229-238. (1952) | MR 0055663

Plebanek G. On the space of continuous function on a dyadic set, Mathematika 38 (1991), 42-49. (1991) | MR 1116683

Plebanek G. Remarks on measurable Boolean algebras and sequential cardinals, Fund. Math. 143 (1993), 11-22. (1993) | MR 1234988 | Zbl 0788.28003

Pasynkov B.A. Sections over zero-dimensional subsets of quotients of locally compact groups (in Russian), Dokl. AN SSSR 178.6 (1968), 1255-1258; English translation in: Soviet Math. Dokl. 9.1 (1968), 281-284. (1968) | MR 0225925

Pontryagin L.S. Topological Groups, Princeton Univ. Press, Princeton, NJ, 1939. | Zbl 0882.01025

Roelcke W.; Dierolf S. Uniform Structures on Topological Groups and Their Quotients, McGraw-Hill, New York, 1981. | MR 0644485 | Zbl 0489.22001

Uspenskiĭ V.V. Real-valued measurable cardinals and sequentially continuous homomorphisms, preprint, December 1993. | MR 1234282

Vaughan J.E. Countably compact spaces and sequentially compact spaces, in: Handbook of Set-theoretical Topology, K. Kunen and J.E. Vaughan eds., North Holland, 1984, pp.569-602. | MR 0776631

Varopoulos N.T. A theorem on the continuity of homomorphisms of locally compact groups, Proc. Cambridge Phil. Soc. 60 (1964), 449-463. (1964) | MR 0162880 | Zbl 0121.03704

Wheeler R.F. A survey on Baire measures and strict topologies, Exp. Math. 2 (1983), 97-190. (1983) | MR 0710569