Geodesic
Continuity of projections of natural bundles
Annales Polonici Mathematici, Tome 57 (1992) no. 2, pp. 105-120.

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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.
DOI : 10.4064/ap-57-2-105-120
Keywords: natural bundle, quasi-natural bundle, regular quasi-natural bundle, locally determined associated space, quasi-prolongation functor

Włodzimierz Mikulski 1

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Włodzimierz Mikulski. Continuity of projections of natural bundles. Annales Polonici Mathematici, Tome 57 (1992) no. 2, pp. 105-120. doi : 10.4064/ap-57-2-105-120. http://geodesic.mathdoc.fr/articles/10.4064/ap-57-2-105-120/

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