# Embedding in a Direct Limit

Rubin, Leonard Roy

• Accepted : 2009.03.10
• Published : 2009.12.31
• 17 7

#### 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.