On Hawaiian Groups of Some Topological Spaces

TL;DR

This paper investigates the structure of Hawaiian groups in various topological spaces, including product, join, cone, and bundle spaces, and explicitly determines the Hawaiian groups of Hawaiian earrings.

Contribution

It provides new insights into the behavior of Hawaiian groups across different topological constructions and explicitly characterizes the Hawaiian groups of Hawaiian earrings.

Findings

Hawaiian groups exhibit specific behaviors under product and join operations.

The structure of Hawaiian groups for cone and bundle spaces is characterized.

The Hawaiian group of the Hawaiian earring space is explicitly determined for all dimensions.

Abstract

The paper is devoted to study the structure of Hawaiian groups of some topological spaces. We present some behaviors of Hawaiian groups with respect to product spaces, weak join spaces, cone spaces, covering spaces and locally trivial bundles. In particular, we determine the structure of the $n$-dimensional Hawaiian group of the $m$-dimensional Hawaiian earring space, for all $1\leq m\leq n$.