The dimension of remainders of rim-compact spaces
Aarts, J. ; Coplakova, E.
Fundamenta Mathematicae, Tome 142 (1993), p. 287-289 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

Answering a question of Isbell we show that there exists a rim-compact space X such that every compactification Y of X has dim(Y)≥ 1.

Publié le : 1993-01-01
EUDML-ID : urn:eudml:doc:212010 
@article{bwmeta1.element.bwnjournal-article-fmv143i3p287bwm,
     author = {J. Aarts and E. Coplakova},
     title = {The dimension of remainders of rim-compact spaces},
     journal = {Fundamenta Mathematicae},
     volume = {142},
     year = {1993},
     pages = {287-289},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv143i3p287bwm}
}

Aarts, J.; Coplakova, E. The dimension of remainders of rim-compact spaces. Fundamenta Mathematicae, Tome 142 (1993) pp. 287-289. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv143i3p287bwm/

[00000] J. M. Aarts and T. Nishiura [1993], Dimension and Extensions, Elsevier, Amsterdam.

[00001] B. Diamond, J. Hatzenbuhler and D. Mattson [1988], On when a 0-space is rimcompact, Topology Proc. 13, 189-202.

[00002] R. Engelking [1989], General Topology, revised and completed edition, Sigma Ser. Pure Math. 6, Heldermann, Berlin.

[00003] J. R. Isbell [1964], Uniform Spaces, Math. Surveys 12, Amer. Math. Soc., Providence, R.I.

[00004] J. Kulesza [1990], An example in the dimension theory of metrizable spaces, Topology Appl. 35, 109-120.

[00005] Yu. M. Smirnov [1958], An example of a completely regular space with zero-dimensional Čech remainder, not having the property of semibicompactness, Dokl. Akad. Nauk SSSR 120, 1204-1206 (in Russian).