On (strongly) ($\Theta$-)discrete homogeneous spaces

TL;DR

This paper introduces and explores classes of (strongly) ($ heta$-)discrete homogeneous spaces, analyzing their relationships with other homogeneity classes and providing examples to distinguish these properties.

Contribution

It defines new classes of homogeneous spaces and investigates their relationships with existing homogeneity concepts, supported by numerous examples.

Findings

Introduced (strongly) ($ heta$-)discrete homogeneous spaces

Established relationships with other homogeneity classes

Provided examples distinguishing different homogeneity types

Abstract

We introduce the classes of (strongly) ($\Theta$-)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.