Displaying similar documents to “Some applications of minimal open sets.”

Minimal Niven numbers

H. Fredricksen, E. J. Ionascu, F. Luca, P. Stănică (2008)

Acta Arithmetica

Similarity:

Two commuting maps without common minimal points

Tomasz Downarowicz (2011)

Colloquium Mathematicae

Similarity:

We construct an example of two commuting homeomorphisms S, T of a compact metric space X such that the union of all minimal sets for S is disjoint from the union of all minimal sets for T. In other words, there are no common minimal points. This answers negatively a question posed in [C-L]. We remark that Furstenberg proved the existence of "doubly recurrent" points (see [F]). Not only are these points recurrent under both S and T, but they recur along the same sequence of powers. Our...

On minimal Hausdorff and minimal Urysohn functions

Filippo Cammaroto, Andrei Catalioto, Jack Porter (2011)

Open Mathematics

Similarity:

In this article, we extend the work on minimal Hausdorff functions initiated by Cammaroto, Fedorchuk and Porter in a 1998 paper. Also, minimal Urysohn functions are introduced and developed. The properties of heredity and productivity are examined and developed for both minimal Hausdorff and minimal Urysohn functions.

C 1 -minimal subsets of the circle

Dusa McDuff (1981)

Annales de l'institut Fourier

Similarity:

Necessary conditions are found for a Cantor subset of the circle to be minimal for some C 1 -diffeomorphism. These conditions are not satisfied by the usual ternary Cantor set.