MP-equivalence of free paratopological groups

作者：Cai, Zhangyong^*; Lin, Shou

来源：Topology and Its Applications, 2017, 215: 35-44.

DOI：10.1016/j.topol.2016.11.004

• Free paratopological group
• Topological isomorphism
• Pseudocompactness
• Hereditary Lindelofness
• Hereditary separability
• Cosmic space

Let FP(X) denote the free paratopological group over a topological space X. Two topological spaces X and Y are called MP-equivalent if FP(X) and FP(Y) are topologically isomorphic. At first, it is shown that there exist non-homeomorphic topological spaces X and Y such that FP(X) and FP(Y) are topologically isomorphic. Secondly, MP-invariance of free paratopological groups is investigated. It is established that pseudocompactness, hereditary Lindelofness, hereditary separability and the property of being a cosmic space are all MP-invariant, which generalizes some conclusions valid for free topological groups to free paratopological groups. Finally, a few questions about MP-equivalence of free paratopological groups are posed.

• 出版日期2017-1-1
• 单位南宁师范大学; 宁德师范学院