The end compactification |Γ| of the locally finite graph Γis the union of the graph and its ends, endowed with a suitable topology. We show that π_1(|Γ|) embeds into a nonstandard free group with hyperfinitely many generators, i.e. an ultraproduct of finitely generated free groups, and that the embedding we construct f…
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This is a survey of several approaches to the framework for working with infinitesimals and infinite numbers, originally developed by Abraham Robinson in the 1960s, and their constructive engagement with the Cantor-Dedekind postulate and the Intended Interpretation hypothesis. We highlight some applications including (…
Stability of Dehn functions proven for ultralimits of Sobolev maps.
problem Stability of Dehn functions under ultralimit of Sobolev maps.
method Using ultralimits of Sobolev maps and properties of ultralimits of Lipschitz maps.
result Stability of Dehn functions under ultraconvergence of pointed length spaces.