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Topologizing Rings of Map Germs: An Order Theoretic Analysis of Germs via Nonstandard Methods
map germ topology nonstandard
2012/6/19
Using nonstandard analysis we define a topology on the ring of germs of functions: $(mathbb R^n,0)\rightarrow(mathbb R,0)$. We prove that this topology is absolutely convex, Hausdorff, that convergent...
Nonstandard Analysis in Topology
nonstandard extension monad transfer principle saturation principle nonstandard hull compactifications realcompactification
2011/9/13
Abstract: We present Nonstandard Analysis by three axioms: the {\em Extension, Transfer and Saturation Principles} in the framework of the superstructure of a given infinite set. We also present sever...
Convexity of Momentum Maps: A Topological Analysis
Convexity of Momentum Maps Topological Analysis
2010/11/15
We extend the Local-to-Global-Principle used in the proof of convexity theorems for momentum maps to not necessarily closed maps $f\colon X\ra Y$ whose target space $Y$ carries a convexity structure ...
Multipole analysis in cosmic topology
Cosmic microwave background cosmology harmonic analysis topology, homotopy
2010/12/16
Low multipole amplitudes in the Cosmic Microwave Background CMB radiation can be explained by selection rules from the underlying multiply-connected homotopy. We apply a multipole analysis to the harm...