Sequential continuity on dyadic compacta and topological groups

 Access to full text

 Full (PDF)

 Access to full text

1. 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) MR0550259
2. Arhangel'skii A.V., On countably compact topologies on compact groups and on dyadic compacta, Top. and Appl. 57 (1994), 163-181. (1994) MR1278022
3. 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) MR0544935
4. AntonovskiĭM., ChudnovskiĭD., Some questions of general topology and Tichonov semifields II., Russian Math. Surveys 31 (1976), 69-128. (1976) 
5. Booth D., A Boolean view of sequential compactness, Fund. Math. 85 (1974), 99-102. (1974) Zbl0297.54020MR0367926
6. Ciesielski K., Real-valued sequentially continuous functions on the product space $2^{\kappa }$, unpublished preprint. 
7. 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) MR1270627
8. 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. Zbl0561.54004MR0776619
9. Engelking R., General Topology, Heldermann Verlag, Berlin, 1989. Zbl0684.54001MR1039321
10. Engelking R., Cartesian products and dyadic spaces, Fund. Math. 57.3 (1965), 287-304. (1965) Zbl0173.50603MR0196692
11. Engelking R., Karłowicz M., Some theorems of set theory and their topological consequences, Fund. Math. 57.3 (1965), 275-285. (1965) MR0196693
12. Fremlin D.H., Measure algebras, in: Handbook of Boolean Algebras, J.D. Monk ed., North Holland, 1989, pp.876-980. Zbl1165.28002MR0991611
13. Fremlin D.H., Real-valued-measurable cardinals, in: Set Theory of the Reals, H. Judah ed., Israel Mathematical Conference Proceedings 6 (1993) 151-304. Zbl0839.03038MR1234282
14. Gryllakis C., Products of completion-regular measures, Proc. Amer. Math. Soc. 103 (1988), 563-568. (1988) Zbl0655.28005MR0943085
15. Hagler J., On the structure of $S$ and $C\left(S\right)$ for $S$ dyadic, Trans. AMS 213 (1975), 415-428. (1975) Zbl0321.46022MR0388062
16. Halmos P.R., Measure Theory, Van Nostrand, New York, 1950. Zbl0283.28001MR0033869
17. Hušek M., Sequentially continuous homomorphisms on products of topological groups, preprint, October 1995. MR1397074
18. Jech T., Set Theory, Academic Press, 1978. Zbl1007.03002MR0506523
19. IvanovskĭL.N., On a hypothesis of P.S. Alexandroff, Dokl. AN SSSR 123.4 (1958), 785-786. (1958) 
20. 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) MR0104753
21. Mazur S., On continuous mappings on Cartesian products, Fund. Math. 39 (1952), 229-238. (1952) MR0055663
22. Plebanek G., On the space of continuous function on a dyadic set, Mathematika 38 (1991), 42-49. (1991) MR1116683
23. Plebanek G., Remarks on measurable Boolean algebras and sequential cardinals, Fund. Math. 143 (1993), 11-22. (1993) Zbl0788.28003MR1234988
24. 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) MR0225925
25. Pontryagin L.S., Topological Groups, Princeton Univ. Press, Princeton, NJ, 1939. Zbl0882.01025
26. Roelcke W., Dierolf S., Uniform Structures on Topological Groups and Their Quotients, McGraw-Hill, New York, 1981. Zbl0489.22001MR0644485
27. Uspenskiĭ V.V., Real-valued measurable cardinals and sequentially continuous homomorphisms, preprint, December 1993. MR1234282
28. 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. MR0776631
29. Varopoulos N.T., A theorem on the continuity of homomorphisms of locally compact groups, Proc. Cambridge Phil. Soc. 60 (1964), 449-463. (1964) Zbl0121.03704MR0162880
30. Wheeler R.F., A survey on Baire measures and strict topologies, Exp. Math. 2 (1983), 97-190. (1983) MR0710569