Hereditary Coreflective Subcategories in Certain Categories of Abelian Semitopological Groups

Veronika Pitrová

doi:10.3390/axioms8030085

Abstract

Let A be an epireflective subcategory of the category of all semitopological groups that consists only of abelian groups. We describe maximal hereditary coreflective subcategories of A that are not bicoreflective in A in the case that the A -reflection of the discrete group of integers is a finite cyclic group, the group of integers with a topology that is not T 0 , or the group of integers with the topology generated by its subgroups of the form p n , where n ∈ N , p ∈ P and P is a given set of prime numbers.

Highlights

By STopGr we denote the category of all semitopological groups and continuous homomorphisms
Our goal is to describe maximal hereditary coreflective subcategories of A that are not bicoreflective in A
Let A be an epireflective subcategory of STopGr such that A ⊆ STopAb and r (Z) is the group of integers with the indiscrete topology

Summary

Introduction

By STopGr we denote the category of all semitopological groups and continuous homomorphisms. If a subcategory D is hereditary and coreflective in A, but not bicoreflective in A, it does not contain the group r (Z). In [4] we presented examples of such epireflective subcategories A of STopGr that every hereditary coreflective subcategory of A that contains a group with a non-indiscrete topology is bicoreflective in A.

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Conclusion