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2. On the multitude of monoidal closed structures on <f>UAP</f>

Author

Lowen, R. and Sioen, M.

Subjects
*HAUSDORFF measures, *COMPACT spaces (Topology), *TOPOLOGICAL spaces, *BLOWING up (Algebraic geometry)
Abstract

In this note, we prove that all compact Hausdorff topological spaces are exponential objects in the category UAP of uniform approach spaces and contractions as introduced in R. Lowen, Approach Spaces: the Missing Link in the Topology-Uniformity-Metric Triad, Oxford University Press, 1997. As a consequence, we show that UAP admits at least as many monoidal closed structures as there are infinite cardinals. We also prove that under the assumption that no measurable cardinals exist, there exists a proper conglomerate of these monoidal closed structures on UAP. [Copyright &y& Elsevier]

Published
2004
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4. On the multitude of monoidal closed structures on UAP

Author

Mark Sioen and Robert Lowen

Subjects
Discrete mathematics, Pure mathematics, Exponential object, Existential quantification, Hausdorff space, Symmetric monoidal category, Monoidal closed structure, Topological space, Closed monoidal category, Rigid class, (Uniform) approach space, Compact Hausdorff space, Geometry and Topology, Link (knot theory), Enriched category, Non-measurable cardinal, Mathematics
Abstract

In this note, we prove that all compact Hausdorff topological spaces are exponential objects in the category UAP of uniform approach spaces and contractions as introduced in R. Lowen, Approach Spaces: the Missing Link in the Topology-Uniformity-Metric Triad, Oxford University Press, 1997. As a consequence, we show that UAP admits at least as many monoidal closed structures as there are infinite cardinals. We also prove that under the assumption that no measurable cardinals exist, there exists a proper conglomerate of these monoidal closed structures on UAP .

Published
2004

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