Search results for "Sierpiński curve"

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On complete metric spaces containing the Sierpinski curve

1998

It is proved that a complete metric space topologically contains the Sierpiński universal plane curve if and only if it has a subset with so-called bypass property, i.e. it has a subset K K containing an arc such that for each a ∈ K a\in K and for each open arc A ⊂ K A\subset K with a ∈ A a\in A , there exists an arbitrary small arc in K ∖ { a } K\setminus \{a\} joining the two components of A ∖ { a } A\setminus \{a\} .

Plane curveApplied MathematicsGeneral MathematicsMathematical analysisComplete metric spaceCombinatoricssymbols.namesakeMetric spaceMathematics Subject ClassificationHomogeneoussymbolsEmbeddingSierpiński curveConnectivityMathematicsProceedings of the American Mathematical Society
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Homeomorphisms of the Sierpinski curve with periodic properties

2013

In this paper, we study the three following types of homeomorphisms of the Sierpinski curve of the two sphere : pointwise periodic, periodic, and almost periodic, and we prove that they are equivalent. We show that a subgroup of homeomorphisms whose orbits are all finite, is a finite subgroup.

PointwiseMathematics::Group Theorysymbols.namesakeGeneral MathematicsMathematical analysissymbolsMathematics::General TopologySierpiński curveComputer Science ApplicationsMathematicsDynamical Systems
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