M. Patrakeev

activity

20142023

most citedMetrizable images of the Sorgenfrey line

6 citations · 6 across the 9 of their papers we have counts for

collaborators

9 papers

math.GN2023

Open images of spaces with a Lusin $π$ -base

Mikhail Patrakeev, Vlad Smolin

In [5] we studied spaces with a Lusin $π$ -base and $π$ -spaces and posed the following question: Does the class of continuous open images of spaces with a Lusin $π$ -base equal the c…

math.LO2023

A Self-Reflecting Formal Language

Mikhail Patrakeev

We construct a formal theory, which we call reflectica, whose language possesses the following properties of natural language: it is a self-reflecting language and an intensional l…

math.GN2022

$π$ -spaces and their open images

Mikhail Patrakeev, Vlad Smolin

We study spaces that can be mapped onto the Baire space (i.e. the countable power of the countable discrete space) by a continuous quasi-open bijection. We give a characterization…

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…

math.GN2016

When the property of having a $π$ -tree is preserved by products

Mikhail Patrakeev

We find sufficient conditions under which the product of spaces that have a $π$ -tree also has a $π$ -tree. These conditions give new examples of spaces with a $π$ -tree: every at mos…

math.GN2015

The complement of a $σ$ -compact subset of a space with a $π$ -tree also has a $π$ -tree

Mikhail Patrakeev

We prove that the complement of a $σ$ -compact subset of a topological space that has a $π$ -tree also has a $π$ -tree. To do this, we construct the foliage hybrid operation, which de…

math.GN2014★ 6 cited

Metrizable images of the Sorgenfrey line

Mikhail Patrakeev

We give descriptions of metrizable topological spaces that are images of the Sorgenfrey line under continuous maps of different types (open, closed, quotient and others). To obtain…

Open images of spaces with a Lusin π-base

A Self-Reflecting Formal Language

π-spaces and their open images

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

When the property of having a π-tree is preserved by products

The complement of a σ-compact subset of a space with a π-tree also has a π-tree

Metrizable images of the Sorgenfrey line

Open images of spaces with a Lusin $π$ -base

$π$ -spaces and their open images

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

When the property of having a $π$ -tree is preserved by products

The complement of a $σ$ -compact subset of a space with a $π$ -tree also has a $π$ -tree