Displaying similar documents to “Invariance of domain in o-minimal structures”

A note on Bierstone-Milman-Pawłucki's paper "Composite differentiable functions"

Krzysztof Jan Nowak (2011)

Annales Polonici Mathematici

Similarity:

We demonstrate that the composite function theorems of Bierstone-Milman-Pawłucki and of Glaeser carry over to any polynomially bounded, o-minimal structure which admits smooth cell decomposition. Moreover, the assumptions of the o-minimal versions can be considerably relaxed compared with the classical analytic ones.

On the implicit function theorem in o-minimal structures

Zofia Ambroży, Wiesław Pawłucki (2015)

Banach Center Publications

Similarity:

A local-global version of the implicit function theorem in o-minimal structures and a generalization of the theorem of Wilkie on covering open sets by open cells are proven.

Michael's theorem for Lipschitz cells in o-minimal structures

Małgorzata Czapla, Wiesław Pawłucki (2016)

Annales Polonici Mathematici

Similarity:

A version of Michael's theorem for multivalued mappings definable in o-minimal structures with M-Lipschitz cell values (M a common constant) is proven. Uniform equi-LCⁿ property for such families of cells is checked. An example is given showing that the assumption about the common Lipschitz constant cannot be omitted.

The Role of Cell-Cell Adhesion in the Formation of Multicellular Sprouts

A. Szabó, A. Czirók (2010)

Mathematical Modelling of Natural Phenomena

Similarity:

Collective cell motility and its guidance via cell-cell contacts is instrumental in several morphogenetic and pathological processes such as vasculogenesis or tumor growth. Multicellular sprout elongation, one of the simplest cases of collective motility, depends on a continuous supply of cells streaming along the sprout towards its tip. The phenomenon is often explained as leader cells pulling the rest of the sprout forward via cell-cell adhesion. Building on an empirically demonstrated...