Partitioning Euclidean space
Copyright policy ) James H. Schmerl;
Partitioning Euclidean space
The author proves the following theorem: For any fixed \(n\)-simplex \(S\) in \(\mathbb{R}^ n\) there exists a partition of \(\mathbb{R}^ n\) into countably many pieces none of which contains an \(n\)-simplex similar to \(S\). The proof uses the Axiom of Choice.
- University of Connecticut United States
partition of \(\mathbb{R}^ n\), Polyhedra and polytopes; regular figures, division of spaces, Axiom of choice and related propositions, Convex sets in \(n\) dimensions (including convex hypersurfaces)
partition of \(\mathbb{R}^ n\), Polyhedra and polytopes; regular figures, division of spaces, Axiom of choice and related propositions, Convex sets in \(n\) dimensions (including convex hypersurfaces)
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selected citations
Citations provided by BIP!
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
Citations provided by BIP!popularityPopularity provided by BIP!
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
Popularity provided by BIP! 6
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Top 10%
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