6533b85cfe1ef96bd12bc806
RESEARCH PRODUCT
On complete metric spaces containing the Sierpinski curve
Janusz R. Prajssubject
Plane curveApplied MathematicsGeneral MathematicsMathematical analysisComplete metric spaceCombinatoricssymbols.namesakeMetric spaceMathematics Subject ClassificationHomogeneoussymbolsEmbeddingSierpiński curveConnectivityMathematicsdescription
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\} .
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1998-01-01 | Proceedings of the American Mathematical Society |