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Inductive limits of free topological groups over metrizable spaces
by
Kohzo Yamada
Shizuoka University
Coauthors: Vladimir G. Pestov
Let A be a cover of a space X. X is called the inductive limit of A if a subset U of X is open (closed) in X whenever U \cap A is open (closed, respectively) in A for each A in A.
Graev proved that the free topological group F(X) and the free abelian topological group A(X) over a compact space X are the inductive limit of { Fn(X) : n in N } and of { An(X) : n in N }, respectively. Then Mack, Morris and Ordman proved the same are true for k\omega-spaces. Furthermore, Tkachenko gave a characterization of a pseudocompact space X such that F(X) is the inductive limit of { Fn(X) : n in N }.
In this talk, we give characterizations of a metrizable space X such that F(X) is the inductive limit of { Fn(X) : n in N } and A(X) is the inductive limit of { An(X) : n in N }, respectively.
Date received: February 9, 1997
Copyright © 1997 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 # caak-31.