Mathematics – General Topology
Scientific paper
2000-10-25
Topology Proceedings, 25 (2000) Summer, 179-206
Mathematics
General Topology
Requires amsart.cls[2000/06/02]; contains one postscript figure
Scientific paper
We recall a characterization of hereditary indecomposability originally obtained by Krasinkiewicz and Minc, and show how it may be used to give unified constructions of various hereditarily indecomposable continua. In particular we answer a question asked by Mackowiak and Tymchatyn by showing that any continuum of arbitrary weight is a weakly confluent image of a hereditarily indecomposable continuum of the same weight. We present two methods of constructing these preimages: (a) by model-theoretic means, using the compactness and completeness theorems from first-order logic to derive these results for continua of uncountable weight from their metric counterparts; and (b) by constructing essential mappings from hereditarily indecomposable continua onto Tychonoff cubes. We finish by reviving an argument due to Kelley about hyperspaces of hereditarily indecomposable continua and show how it leads to a point-set argument that reduces Brouwer's Fixed-point theorem to its three-dimensional version.
Hart Klaas Pieter
Mill Jan van
Pol Roman
No associations
LandOfFree
Remarks on hereditarily indecomposable continua does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Remarks on hereditarily indecomposable continua, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Remarks on hereditarily indecomposable continua will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-105718