Approximation of maps into the Lipscomb space by embeddings
by
Uroš Milutinović
University of Maribor, Slovenia

Let J(\tau) be the Lipscomb one-dimensional space and L_n(\tau) subset or equal J(\tau)ⁿ⁺¹ the Lipscomb n-dimensional universal space of weight \tau >= \aleph₀. We prove the following theorem: Let X be a metrizable space, dimX <= n, w X <= \tau, f:X --> J(\tau)ⁿ⁺¹ a continuous map, and \epsilon a positive number. Then there is an embedding \psi:X --> L_n(\tau) such that d(f, \psi) <= \epsilon. Also, in the separable case an analogous result is obtained, in which the classic triangular Sierpi\'nski curve (homeomorphic to J(3)) is used instead of J(\aleph₀) (strengthening the results of Ivan Ivansi\'c and Uros Milutinovi\'c: A Universal Separable Metric Space of Lipscomb Type ).

Date received: March 15, 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 # caex-28.