Approximating a k-dimensional continuum with k-dimensional finite T₀-spaces
by
Ralph Kopperman
City College of CUNY
Coauthors: Richard G. Wilson (UAM, Mexico, DF, MEXICO)

In previous work, we showed that:

Compact Hausdorff spaces are precisely the Hausdorff reflections of inverse limits of finite T₀-spaces and continuous maps,

(with Judy Kennedy) Chainable continua are precisely the Hausdorff reflections of inverse limits of finite COTS and separating maps; here a continuous map is separating if inverse images of distinct closed points lie in disjoint open sets,

(with I. Puga) One-dimensional continua are precisely the Hausdorff reflections of inverse limits of finite T_1/2-spaces (those in which all points are open or closed) and separating maps,

Here we discuss a similar representation of k-dimensional continua: k-Dimensional continua are precisely the Hausdorff reflections of inverse limits of finite k-dimensional T₀-spaces and chaining maps; here a continuous map is chaining if the image of the closure of each point is a specialization chain.

Date received: July 5, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeu-59.