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Non-normality, topological transitivity and expanding families Meyrath, Thierry ; in Mathematical Proceedings of the Cambridge Philosophical Society (2022), 173(3), 511-523 We investigate the behaviour of families of meromorphic functions in the neighbourhood of points of non-normality and prove certain covering properties that complement Montel’s Theorem. In particular, we ... [more ▼] We investigate the behaviour of families of meromorphic functions in the neighbourhood of points of non-normality and prove certain covering properties that complement Montel’s Theorem. In particular, we also obtain characterisations of non-normality in terms of such properties. [less ▲] Detailed reference viewed: 54 (2 UL)Simplicial localization of homotopy algebras over a prop Yalin, Sinan in Mathematical Proceedings of the Cambridge Philosophical Society (2014), 157(3), 457468 We prove that a weak equivalence between two cofibrant (colored) props in chain complexes induces a Dwyer-Kan equivalence between the simplicial localizations of the associated categories of algebras ... [more ▼] We prove that a weak equivalence between two cofibrant (colored) props in chain complexes induces a Dwyer-Kan equivalence between the simplicial localizations of the associated categories of algebras. This homotopy invariance under base change implies that the homotopy category of homotopy algebras over a prop P does not depend on the choice of a cofibrant resolution of P, and gives thus a coherence to the notion of algebra up to homotopy in this setting. The result is established more generally for algebras in combinatorial monoidal dg categories. [less ▲] Detailed reference viewed: 38 (0 UL) |
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