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2022•arXiv (Cornell University)Open access

On (strongly) ($Θ$-)discrete homogeneous spaces

Vitaly Chatyrko, Alexandre Karassev

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Abstract

We introduce the classes of (strongly) ($Θ$-)discrete homogeneous spaces. We discuss the relationships of these classes to other classes of spaces possessing homogeneity-related properties, such as (strongly) ($n$-)homogeneous spaces. Many examples are given distinguishing discrete homogeneity and other types of homogeneity.

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We introduce the classes of (strongly) ($Θ$-)discrete homogeneous spaces. We discuss the relationships of these classes to other classes of spaces possessing homogeneity-related properties, such as (strongly) ($n$-)homogeneous spaces. Many examples are given distinguishing discrete homogeneity and other types of homogeneity.

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Available abstract

We introduce the classes of (strongly) ($Θ$-)discrete homogeneous spaces. We discuss the relationships of these classes to other classes of spaces possessing homogeneity-related properties, such as (strongly) ($n$-)homogeneous spaces. Many examples are given distinguishing discrete homogeneity and other types of homogeneity.

Key concepts: Homogeneity (statistics), Homogeneous, Mathematics, Pure mathematics, Homogeneous space, Combinatorics, Geometry, Statistics

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