Vol. 101, No. 2, 1982

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 331: 1  2
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
On compactifications of metric spaces with transfinite dimensions

Leonid A. Luxemburg

Vol. 101 (1982), No. 2, 399–450
Abstract

In this paper we prove that every separable metric space X with transfinite dimension IndX has metric compactification cX such that

Ind cX = Ind X,  ind cX = ind X, D (cX ) = D (X),

where ind X (Ind X) denotes small (large) inductive transfinite dimension, and D(X) denotes the transfinite D-dimension. More generally, let T be a set of invariants (ind,Ind,D). We consider the following problem:

Let R T and X be a metric space. Does there exist a bicompactum (complete space) cX X such that

μ(X ) = μ(cX) for μ ∈ R.

When it is not so, we give counterexamples. We give also necessary and sufficient conditions of the existence of transfinite dimensions of separable metric space in terms of compactifications.

Mathematical Subject Classification 2000
Primary: 54F45
Milestones
Received: 5 March 1979
Revised: 12 February 1981
Published: 1 August 1982
Authors
Leonid A. Luxemburg