# Continuity of projections of natural bundles

Annales Polonici Mathematici (1992)

- Volume: 57, Issue: 2, page 105-120
- ISSN: 0066-2216

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topWłodzimierz M. Mikulski. "Continuity of projections of natural bundles." Annales Polonici Mathematici 57.2 (1992): 105-120. <http://eudml.org/doc/262285>.

@article{WłodzimierzM1992,

abstract = {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.},

author = {Włodzimierz M. Mikulski},

journal = {Annales Polonici Mathematici},

keywords = {natural bundle; quasi-natural bundle; regular quasi-natural bundle; locally determined associated space; quasi-prolongation functor; manifold; prolongation functors},

language = {eng},

number = {2},

pages = {105-120},

title = {Continuity of projections of natural bundles},

url = {http://eudml.org/doc/262285},

volume = {57},

year = {1992},

}

TY - JOUR

AU - Włodzimierz M. Mikulski

TI - Continuity of projections of natural bundles

JO - Annales Polonici Mathematici

PY - 1992

VL - 57

IS - 2

SP - 105

EP - 120

AB - 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.

LA - eng

KW - natural bundle; quasi-natural bundle; regular quasi-natural bundle; locally determined associated space; quasi-prolongation functor; manifold; prolongation functors

UR - http://eudml.org/doc/262285

ER -

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