DIRECT LIMIT TOPOLOGIES OF QUASI-UNIFORM SPACES AND PARATOPOLOGICAL GROUPS

作者：Lin, Fucai^*; Xie, Li-Hong; Zhang, Jing

来源：Banach Journal of Mathematical Analysis, 2016, 10(1): 48-70.

DOI：10.1215/17358787-3163248

• direct limit
• quasi-uniform spaces
• paratopological groups
• quasi-pseudometric
• semitopological groups

Given an increasing sequence (X-n)(n is an element of omega) of quasi-uniform spaces and paratopological groups, we study the topology of the direct limits qu-<(lim)under right arrow>X-n and pg-<(lim)under right arrow>X-n of the sequence X-n)(n is an element of omega) in the categories of quasi-uniform spaces and paratopological groups, respectively. First, we prove that the quasi uniformity of the quasi -uniform direct limit qu-lim X is generated by some special family of quasi-pseudometrics. Then we discuss some properties of the direct limits pg-<(lim)under right arrow>X-n. Finally, we give an explicit description of the topology of the direct limit pg-<(lim)under right arrow>X-n under certain conditions on the sequence of paratopological groups ((X-n)(n is an element of omega). Moreover, some questions about direct limits of qu-<(lim)under right arrow>X-n and pg-<(lim)under right arrow>X-n are posed.

• 出版日期2016-1
• 单位五邑大学; 闽南师范大学