Some results about tri difference paracompactness theorems and applications
Résumé
We present a comprehensive extension of Difference (D-) paracompactness to tri‑topological spaces—sets endowed with three independent topologies. The paper contributes ten new theorems that characterise the behaviour of tri‑D‑paracompact spaces under products, subspaces, perfect mappings, inverse limits, and covering‑dimension constraints. We introduce two gradations—σ‑tri‑D‑paracompactness and λ‑tri‑D‑paracompactness—and prove their strictness via explicit counter‑examples. Applications to multi‑metric data analysis and dimensionality reduction are sketched. All proofs are original and written to minimise dependence on external axioms beyond ZFC.
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Références
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