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arXiv · 2504.19425

Fibrewise compactifications and generalised limits in commutative and noncommutative topology

Alexander Mundey
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Abstract

We introduce fibrewise compactifications in both the setting of locally compact Hausdorff spaces and continuous maps, and the parallel setting of $C^*$-algebras and nondegenerate multiplier-valued $*$-homomorphisms. In both situations, we use fibrewise compactifications to define regulated limits. In the topological setting, regulated limits extend classical inverse limits so that the resulting limit space remains locally compact; examples include the path spaces of directed graphs. In the operator-algebraic setting, regulated limits realise a direct-limit construction for multiplier-valued $*$-homomorphisms; examples include the cores of relative Cuntz-Pimsner algebras.

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Alexander Mundey. 2025-04-28. Fibrewise compactifications and generalised limits in commutative and noncommutative topology. https://arxiv.org/abs/2504.19425

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