TL;DR
This paper characterizes Berlanga's topology on measure homology of CW-complexes, demonstrating it is Hausdorff, thereby resolving a previously posed question and clarifying the topological structure of measure homology.
Contribution
It provides a complete characterization of Berlanga's topology on measure homology, showing it is Hausdorff, which was previously unknown.
Findings
Berlanga's topology on measure homology is Hausdorff.
The characterization applies to CW-complexes.
Answers a question posed by Berlanga.
Abstract
Measure homology was introduced by Thurston in order to compute the simplicial volume of hyperbolic manifolds. Berlanga endowed measure homology with a structure of graded locally convex (possibly non-Hausdorff) topological vector space. In this note we completely characterize Berlanga's topology on measure homology of CW-complexes, showing in particular that it is Hausdorff. This answers a question posed by Berlanga.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology