Metrization of additive $\kappa$-metric spaces
HTML articles powered by AMS MathViewer
- by Takesi Isiwata PDF
- Proc. Amer. Math. Soc. 100 (1987), 164-168 Request permission
Abstract:
We prove that an additive $\kappa$-metric space $X$ is metrizable if $X$ is one of the following: (1) $X$ is pseudocompact, (2) $X$ is a $wM$-space, (3) $X$ is a paracompact $\beta$-space, especially stratifiable.References
- R. H. Bing, Metrization of topological spaces, Canad. J. Math. 3 (1951), 175β186. MR 43449, DOI 10.4153/cjm-1951-022-3
- Carlos J. R. Borges, On stratifiable spaces, Pacific J. Math. 17 (1966), 1β16. MR 188982, DOI 10.2140/pjm.1966.17.1
- Carlos J. R. Borges, On metrizability of topological spaces, Canadian J. Math. 20 (1968), 795β804. MR 231355, DOI 10.4153/CJM-1968-078-1
- Jack G. Ceder, Some generalizations of metric spaces, Pacific J. Math. 11 (1961), 105β125. MR 131860, DOI 10.2140/pjm.1961.11.105
- Geoffrey D. Creede, Concerning semi-stratifiable spaces, Pacific J. Math. 32 (1970), 47β54. MR 254799, DOI 10.2140/pjm.1970.32.47 A. N. DraniΕ‘nikov, Simultaneous annihilator of families of closed sets, $\kappa$-metrizable and stratifiable spaces, Soviet Math. Dokl. 19 (1978), 1466-1469.
- A. H. Frink, Distance functions and the metrization problem, Bull. Amer. Math. Soc. 43 (1937), no.Β 2, 133β142. MR 1563501, DOI 10.1090/S0002-9904-1937-06509-8
- Geoffrey D. Creede, Concerning semi-stratifiable spaces, Pacific J. Math. 32 (1970), 47β54. MR 254799, DOI 10.2140/pjm.1970.32.47
- Robert W. Heath, Arc-wise connectedness in semi-metric spaces, Pacific J. Math. 12 (1962), 1301β1319. MR 166759, DOI 10.2140/pjm.1962.12.1301
- R. W. Heath, A paracompact semi-metric space which is not an $M_{3}$-space, Proc. Amer. Math. Soc. 17 (1966), 868β870. MR 195051, DOI 10.1090/S0002-9939-1966-0195051-9
- R. E. Hodel, Moore spaces and $w$ $\Delta$-spaces, Pacific J. Math. 38 (1971), 641β652. MR 307169, DOI 10.2140/pjm.1971.38.641
- R. E. Hodel, Metrizability of topological spaces, Pacific J. Math. 55 (1974), 441β459. MR 370520, DOI 10.2140/pjm.1974.55.441
- Tadashi Ishii, On $wM$-spaces. I, II, Proc. Japan Acad. 46 (1970), 5-10; ibid. 46 (1970), 11β15. MR 0261534
- Tadashi Ishii and Takanori Shiraki, Some properties of $wM$-spaces, Proc. Japan Acad. 47 (1971), 167β172. (loose addendum). MR 293581
- Kiiti Morita, Products of normal spaces with metric spaces, Math. Ann. 154 (1964), 365β382. MR 165491, DOI 10.1007/BF01362570 E. V. Ε Δepin, On topological products, groups and a new class of spaces more general than metric spaces, Soviet Math. Dokl. 17 (1976), 152-155.
- E. V. Ε Δepin, Topology of limit spaces with uncountable inverse spectra, Uspehi Mat. Nauk 31 (1976), no.Β 5 (191), 191β226 (Russian). MR 0464137 β, On $\kappa$-metrizable spaces, Math. USSR-Izv. 14 (1980), 407-440.
- J. Suzuki, K. Tamano, and Y. Tanaka, $\kappa$-metrizable spaces, stratifiable spaces and metrization, Proc. Amer. Math. Soc. 105 (1989), no.Β 2, 500β509. MR 933521, DOI 10.1090/S0002-9939-1989-0933521-9
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 100 (1987), 164-168
- MSC: Primary 54E20; Secondary 54E30, 54E35
- DOI: https://doi.org/10.1090/S0002-9939-1987-0883422-8
- MathSciNet review: 883422