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Investigates branched coverings and conditional expectations in topology, highlighting recent advancements.
We address the problem of identification of branched coverings (continuous open surjections p Y→ X of Hausdorff spaces with uniformly bounded number of pre-images) with faithful unital positive conditional expectations E C(Y)→ C(X) topologically of index-finite type. Caused by recent progress (A. Chirvasitu, 2024) in the field and detection of an issue in our old paper, we revisit it to make some advances.
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Evgenij Troitsky (2026) studied this question.
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