We discuss the exactness of estimates in the finite sum theorems for transfinite inductive dimensions trind and trInd. The technique obtained gives an opportunity to repeat and sometimes strengthen some well known results about compacta with trind ≠ trInd. In particular we improve an estimate of the small transfinite inductive dimension of Smirnov’s compacta , given by Luxemburg [Lu2].
@article{bwmeta1.element.bwnjournal-article-fmv162i1p91bwm,
author = {Vitalij Chatyrko},
title = {On finite sum theorems for transfinite inductive dimensions},
journal = {Fundamenta Mathematicae},
volume = {159},
year = {1999},
pages = {91-98},
zbl = {0938.54031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv162i1p91bwm}
}
Chatyrko, Vitalij. On finite sum theorems for transfinite inductive dimensions. Fundamenta Mathematicae, Tome 159 (1999) pp. 91-98. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv162i1p91bwm/
[00000] [Ch] V. A. Chatyrko, Ordinal products of topological spaces, Fund. Math. 144 (1994), 95-117. | Zbl 0809.54027
[00001] [Ch-K] V. A. Chatyrko and K. L. Kozlov, On ( transfinite) small inductive dimension of products, preprint, 1999.
[00002] [E] R. Engelking, Theory of Dimensions, Finite and Infinite, Heldermann Verlag, Lemgo, 1995. | Zbl 0872.54002
[00003] [F] V. V. Filippov, A bicompactum with noncoinciding inductive dimensions, Soviet Math. Dokl. 10 (1969), 208-211. | Zbl 0186.27002
[00004] [Le] B. T. Levshenko, Spaces of transfinite dimensions, Mat. Sb. 67 (1965), 225-266 (in Russian).
[00005] [Lu1] L. A. Luxemburg, Compacta with noncoinciding transfinite dimensions, Soviet Math. Dokl. 14 (1973), 1593-1597. | Zbl 0292.54044
[00006] [Lu2] L. A. Luxemburg, On compact metric spaces with noncoinciding transfinite dimensions, Pacific J. Math. 93 (1981), 339-386. | Zbl 0397.54048
[00007] [S] Ju. M. Smirnov, On universal spaces for certain classes of infinite-dimensional spaces, Izv. Akad. Nauk SSSR 23 (1959), 185-196 (in Russian). | Zbl 0086.36804