Even in the locally connected case there are several non isomorphic trivialization structures. The difference is that, in that case, there is a canonical one.
Date: Wed, 6 Oct 2010 09:34:51 -0300 From: edubuc@dm.uba.ar To: edubuc@dm.uba.ar CC: categories@mta.ca Subject: categories: errata
The difference is only manifest when the space B is not locally connected. In this case we may have homeomorphisms from X to X over B which do not preserve this structure (Spanier, Algebraic Topology).
is not quite it should be,
there is a clear notion of isomorphism of trivialization structure, and a same space X over B may have non isomorphic structures. Alternatively, a continuous function over B does not necessarily preserve the trivialization structures.
however, if B is locally connected, trivialization structures are like a pure property of X.
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