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Covering spaces and irreducible partitions

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Grubb D.

Fundamenta Mathematicae

2011

tom 211

nr 1

77-84

An irreducible partition of a space is a partition of that space into solid sets with a certain minimality property. Previously, these partitions were studied using the cup product in cohomology. This paper obtains similar results using the fundamental group instead. This allows the use of covering spaces to obtain information about irreducible partitions. This is then used to generalize Knudsen's construction of topological measures on the torus. We give examples of such measures that are invariant under Hamiltonian flows on certain symplectic manifolds.

Quasi-linear maps

100%

Grubb D.

Fundamenta Mathematicae

2008

tom 198

nr 1

1-15

A quasi-linear map from a continuous function space C(X) is one which is linear on each singly generated subalgebra. We show that the collection of quasi-linear functionals has a Banach space pre-dual with a natural order. We then investigate quasi-linear maps between two continuous function spaces, classifying them in terms of generalized image transformations.

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2 Fundamenta Mathematicae

2 Grubb D.

1 2011

1 2008

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Covering spaces and irreducible partitions

Quasi-linear maps