Yuri Borysovych Zelinskii

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Questions related from Yuri Borysovych Zelinskii

Can there be a sphere in a Euclidean space linearly convex set?

Definition. A set E ⊂ Rn in real Euclidean space is called to be m-convex (m < n) if for each x ∈ Rn \ E there exists an m-dimensional plane L(x) such that x ∈ L(x) and L(x) ∩ E = ∅. In a...

24 September 2015 6,116 2 View

Is it true, that next Jordan curve be a circle?

Let C be closed Jordan curve in R 2 and for arbitrary circle L from property that intersection C ∩L contains 3 points follows, that C ∩L contains no less then 4 points. Is it true, that C also be...

29 May 2015 4,872 8 View

Does mapping exist for an n-dimensional projective space in an n-dimensional sphere where every point of image has no more than 2 preimages for n>3?

Detail see in On a mapping of a projective space into a sphere//Ukrainian Mathematical Journal 12/2010; 62(7):1090-1097

18 April 2015 1,241 2 View