Free paratopological groups

2012/12/23 by Ali Sayed Elfard, Elfard, Ali Sayed · 2 citations
Decision Sciences · Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #math.GN

paper · pdf · doi:10.48550/arxiv.1212.5749

openalex publication_date 2012/12/23 · arxiv created 2013/11/14 · arxiv updated 2013/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Let \FP(X) be the free paratopological group on a topological space X in the sense of Markov. In this paper, we study the group \FP(X) on a P_α-space X where α is an infinite cardinal and then we prove that the group \FP(X) is an Alexandroff space if X is an Alexandroff space. Moreover, we introduce a neighborhood base at the identity of the group \FP(X) when the space X is Alexandroff and then we give some properties of this neighborhood base. As applications of these, we prove that the group \FP(X) is T₀ if X is T₀, we characterize the spaces X for which the group \FP(X) is a topological group and then we give a class of spaces X for which the group \FP(X) has the inductive limit property.

Cited by

• The mapping i₂ on the free paratopological groups
• The countable type properties in free paratopological groups

Related

• Neighborhood base at the identity of free paratopological groups
• On the topology of free paratopological groups. II
• The mapping i₂ on the free paratopological groups
• The countable type properties in free paratopological groups
• On pseudobounded and premeager paratopological groups