This paper is a contribution to the axiomatic approach to geometric objects. A collection of a manifold M, a topological space N, a group homomorphism E: Diff(M) → Homeo(N) and a function π: N → M is called a quasi-natural bundle if (1) π ∘ E(f) = f ∘ π for every f ∈ Diff(M) and (2) if f,g ∈ Diff(M) are two diffeomorphisms such that f|U = g|U for some open subset U of M, then E(f)|π^{-1}(U) = E(g)|π^{-1}(U). We give conditions which ensure that π: N → M is continuous. In particular, if (M,N,E,π) is a quasi-natural bundle with N Hausdorff, then π is continuous. Using this result, we classify (quasi) prolongation functors with compact fibres.
@article{bwmeta1.element.bwnjournal-article-apmv57z2p105bwm,
author = {W\l odzimierz M. Mikulski},
title = {Continuity of projections of natural bundles},
journal = {Annales Polonici Mathematici},
volume = {57},
year = {1992},
pages = {105-120},
zbl = {0812.55008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv57z2p105bwm}
}
Włodzimierz M. Mikulski. Continuity of projections of natural bundles. Annales Polonici Mathematici, Tome 57 (1992) pp. 105-120. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv57z2p105bwm/
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