Dimension of stratifiable spaces

Oka, Shinpei

doi:10.1090/S0002-9947-1983-0678346-6

Dimension of stratifiable spaces
HTML articles powered by AMS MathViewer

by Shinpei Oka PDF

Trans. Amer. Math. Soc. 275 (1983), 231-243 Request permission

Abstract:

We define a subclass, denoted by $E{M_3}$, of the class of stratifiable spaces, and obtain several dimension theoretical results for $E{M_3}$ including the coincidence theorem for dim and Ind. The class $E{M_3}$ is countably productive, hereditary, preserved under closed maps and, furthermore, the largest subclass of stratifiable spaces in which a harmonious dimension theory can be established.

References

Carlos J. R. Borges, On stratifiable spaces, Pacific J. Math. 17 (1966), 1–16. MR 188982
Jack G. Ceder, Some generalizations of metric spaces, Pacific J. Math. 11 (1961), 105–125. MR 131860
Geoffrey D. Creede, Concerning semi-stratifiable spaces, Pacific J. Math. 32 (1970), 47–54. MR 254799
Ryszard Engelking, Teoria wymiaru, Biblioteka Matematyczna, Tom 51. [Mathematics Library, Vol. 51], Państwowe Wydawnictwo Naukowe, Warsaw, 1977 (Polish). MR 0482696
Gary Gruenhage, Stratifiable spaces are $M_{2}$, Topology Proceedings, Vol. I (Conf., Auburn Univ., Auburn, Ala., 1976) Math. Dept., Auburn Univ., Auburn, Ala., 1977, pp. 221–226. MR 0448307

Stratifiable spaces are

spaces

16

Munehiko It\B{o}, Weak $L$-spaces are free $L$-spaces, J. Math. Soc. Japan 34 (1982), no. 3, 507–514. MR 659619, DOI 10.2969/jmsj/03430507
Heikki J. K. Junnila, Neighbornets, Pacific J. Math. 76 (1978), no. 1, 83–108. MR 482677
N. Lašnev, On continuous decompositions and closed mappings of metric spaces, Dokl. Akad. Nauk SSSR 165 (1965), 756–758 (Russian). MR 0192478

On the equality of dimensions for closed images of metric spaces

15

On closed images of metric spaces

16

Kiiti Morita, A condition for the metrizability of topological spaces and for $n$-dimensionality, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 5 (1955), 33–36. MR 71754
Keiô Nagami, Normality of products, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 33–37. MR 0428250
Keiô Nagami, Perfect class of spaces, Proc. Japan Acad. 48 (1972), 21–24. MR 307207
Keiô Nagami, The equality of dimensions, Fund. Math. 106 (1980), no. 3, 239–246. MR 584496, DOI 10.4064/fm-106-3-239-246
Keiô Nagami, Dimension of free $L$-spaces, Fund. Math. 108 (1980), no. 3, 211–224. MR 594319, DOI 10.4064/fm-108-3-211-224
Shinpei Oka, A note on the covering dimension of Lašnev spaces, Proc. Japan Acad. Ser. A Math. Sci. 54 (1978), no. 3, 73–75. MR 482688
Shinpei Oka, Dimension of finite unions of metric spaces, Math. Japon. 24 (1979/80), no. 4, 351–362. MR 557465
Shinpei Oka, Every Lašnev space is the perfect image of a zero-dimensional one, Bull. Acad. Polon. Sci. Sér. Sci. Math. 28 (1980), no. 11-12, 591–594 (1981) (English, with Russian summary). MR 628647
Shinpei Oka, Free patched spaces and fundamental theorems of dimension theory, Bull. Acad. Polon. Sci. Sér. Sci. Math. 28 (1980), no. 11-12, 595–602 (1981) (English, with Russian summary). MR 628648
Shinpei Oka, An inequality concerning three fundamental dimensions of paracompact $\sigma$-spaces, Proc. Amer. Math. Soc. 83 (1981), no. 4, 790–792. MR 630056, DOI 10.1090/S0002-9939-1981-0630056-0
Akihiro Okuyama, Some generalizations of metric spaces, their metrization theorems and product spaces, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 9 (1968), 236–254 (1968). MR 230283
B. A. Pasynkov, On the spectral decomosition of topological spaces, Mat. Sb. (N.S.) 66 (108) (1965), 35–79 (Russian). MR 0172236
A. R. Pears, Dimension theory of general spaces, Cambridge University Press, Cambridge, England-New York-Melbourne, 1975. MR 0394604
F. G. Slaughter Jr., The closed image of a metrizable space is $M_{1}$, Proc. Amer. Math. Soc. 37 (1973), 309–314. MR 310832, DOI 10.1090/S0002-9939-1973-0310832-X
Frank Siwiec and Jun-iti Nagata, A note on nets and metrization, Proc. Japan Acad. 44 (1968), 623–627. MR 242116