Abstract:A characterization of metrizability in dyadic spaces in terms of sequential continuity is given. Also, it is shown by examples that invariance under projections (composition) cannot be eliminated from the hypotheses of theorems of Mazur and Engelking concerning the continuity of sequentially continuous functions.
- B. A. Efimov, Dyadic bicompacta, Trudy Moskov. Mat. Obšč. 14 (1965), 211–247 (Russian). MR 0202105
- R. Engelking, On functions defined on Cartesian products, Fund. Math. 59 (1966), 221–231. MR 203697, DOI 10.4064/fm-59-2-221-231
- R. H. Marty, $m$-adic spaces, Acta Math. Acad. Sci. Hungar. 22 (1971/72), 441–447. MR 293572, DOI 10.1007/BF01896441 —, Metrizability of dyadic spaces, Notices Amer. Math. Soc. 22 (1975), A-653. Abstract #75T-G101.
- S. Mazur, On continuous mappings on Cartesian products, Fund. Math. 39 (1952), 229–238 (1953). MR 55663, DOI 10.4064/fm-39-1-229-238
- S. Mrówka, Mazur theorem and $m$-adic spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 18 (1970), 299–305 (English, with Russian summary). MR 264613
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 66 (1977), 363-364
- MSC: Primary 54C05; Secondary 54D55, 54E35
- DOI: https://doi.org/10.1090/S0002-9939-1977-0500813-9
- MathSciNet review: 0500813