M. Patrakeev

collaborators

3 papers

math.GN2020

Reverse induction proof of D property of the countable power of the Sorgenfrey line

Mikhail Patrakeev

We present a new method of proof, which we call reverse induction. This method allows to establish certain properties of a product $\prod_{i = 0}^{\infty} X_{i}$ by making a kind…

math.GN2018

A space with a Lusin $π$ -base whose square has no Lusin $π$ -base

Mikhail Patrakeev

We construct a space $X$ that has a Lusin $π$ -base and such that $X^{2}$ has no Lusin $π$ -base.

math.GN2018

A simple closed curve in $R^{3}$ whose convex hull equals the half-sum of the curve with itself

Mikhail Patrakeev

If $Γ$ is the range of a Jordan curve that bounds a convex set in $R^{2},$ then $\frac{1}{2} (Γ + Γ) = co (Γ),$ where $+$ is the Minkowski sum and $co$ is the co…

Reverse induction proof of D property of the countable power of the Sorgenfrey line

A space with a Lusin π-base whose square has no Lusin π-base

A simple closed curve in R3 whose convex hull equals the half-sum of the curve with itself

A space with a Lusin $π$ -base whose square has no Lusin $π$ -base

A simple closed curve in $R^{3}$ whose convex hull equals the half-sum of the curve with itself