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Embedding in a Direct Limit

Rubin, Leonard Roy

  • Received : 2008.11.13
  • Accepted : 2009.03.10
  • Published : 2009.12.31

Abstract

Let X be a direct system of topological spaces and X its direct limit. We show that under certain conditions the direct limit of a "subsystem" of X embeds in a canonical way as a closed subspace of X.

Keywords

closed embedding;cofinite;direct limit;direct spectrum;direct system;directed set;embedding conditions

References

  1. J. Dugundji, Topology, Allyn and Bacon, Inc., Boston, 1968.
  2. S. Mardesic and L. Rubin, A note on extension theory and direct limits, to appear in Publicationes Debrecen.