Detecting topological groups which are (locally) homeomorphic to LF-spaces
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文摘
We prove that a topological group G is (locally) homeomorphic to an LF-space if for some increasing sequence of subgroups such that
- (1)
for any neighborhoods , , of the neutral element , the set is a neighborhood of e in G;
- (2)
each group is (locally) homeomorphic to a Hilbert space;
- (3)
for every the quotient map is a locally trivial bundle;
- (4)
for infinitely many numbers each Z-point in the quotient space is a strong Z-point.