Universal spaces for locally finite-dimensional Tychonoff spaces

Universal spaces for locally finite-dimensional Tychonoff spaces
HTML articles powered by AMS MathViewer

by M. G. Charalambous PDF

Proc. Amer. Math. Soc. 106 (1989), 507-514 Request permission

We prove that the class of all locally finite-dimensional Tychonoff spaces and other related classes have universal elements.

References

Factorization of mappings according to weight and dimension

8

M. G. Charalambous, A new covering dimension function for uniform spaces. 2, J. London Math. Soc. (2) 11 (1975), no. part, 137–143. MR 375258, DOI 10.1112/jlms/s2-11.2.137

Further theory and applications of covering dimension of uniform spaces

C. H. Dowker, Local dimension of normal spaces, Quart. J. Math. Oxford Ser. (2) 6 (1955), 101–120. MR 86286, DOI 10.1093/qmath/6.1.101
Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna, Tom 47. [Mathematics Library. Vol. 47]. MR 0500779
Ryszard Engelking, Teoria wymiaru, Biblioteka Matematyczna, Tom 51. [Mathematics Library, Vol. 51], Państwowe Wydawnictwo Naukowe, Warsaw, 1977 (Polish). MR 0482696
Leonid Luxemburg, On universal metric locally finite-dimensional spaces, General Topology Appl. 10 (1979), no. 3, 283–290. MR 546101, DOI 10.1016/0016-660x(79)90040-0

On universal bicompacta of a given weight and dimension

5

A factorization theorem for non-closed sets

13

B. A. Pasynkov, Factorization theorems in dimension theory, Uspekhi Mat. Nauk 36 (1981), no. 3(219), 147–175, 256 (Russian). MR 622723
B. A. Pasynkov, On dimension theory, Aspects of topology, London Math. Soc. Lecture Note Ser., vol. 93, Cambridge Univ. Press, Cambridge, 1985, pp. 227–250. MR 787831
A. R. Pears, Dimension theory of general spaces, Cambridge University Press, Cambridge, England-New York-Melbourne, 1975. MR 0394604
B. R. Wenner, A universal separable metric locally finite-dimensional space, Fund. Math. 80 (1973), no. 3, 283–286. MR 341444, DOI 10.4064/fm-80-3-283-286