A non-omega-balanced paratopological group with countable pi-character

作者：Sheng, Li-Hong^*; Shi, Wei-Xue

来源：Topology and Its Applications, 2017, 222: 115-120.

DOI：10.1016/j.topol.2017.03.003

• Paratopological group
• omega-Narrow
• omega-Balanced
• Saturated
• Weak extent

In this paper, we mainly prove that if G is a saturated paratopological group with we(G) <= kappa, where kappa is an infinite cardinal, then G is kappa-narrow. It gives a partial answer to the problem posed by Sanchez in [10, Problem 2.24] and even more. Applying this property, we show that if G is a saturated Hausdorff paratopological group with we(G)pi chi(G) <= omega, then G can be condensed onto a Hausdorff space with a countable base. Also, we construct a Hausdorff paratopological group with countable pi-character, but it is not omega-balanced. This gives a negative answer to the problem posed by Sanchez in [9, Problem 2.13].

• 出版日期2017-5-15
• 单位南京大学