Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 10, Number 1 (2016), 48-70.
Direct limit topologies of quasi-uniform spaces and paratopological groups
Given an increasing sequence of quasi-uniform spaces and paratopological groups, we study the topology of the direct limits - and - of the sequence in the categories of quasi-uniform spaces and paratopological groups, respectively. First, we prove that the quasi-uniformity of the quasi-uniform direct limit - is generated by some special family of quasi-pseudometrics. Then we discuss some properties of the direct limits -. Finally, we give an explicit description of the topology of the direct limit - under certain conditions on the sequence of paratopological groups . Moreover, some questions about direct limits of - and - are posed.
Banach J. Math. Anal., Volume 10, Number 1 (2016), 48-70.
Received: 26 June 2014
Accepted: 7 April 2015
First available in Project Euclid: 15 October 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 46A13: Spaces defined by inductive or projective limits (LB, LF, etc.) [See also 46M40]
Secondary: 22A05: Structure of general topological groups 54B30: Categorical methods [See also 18B30] 54E15: Uniform structures and generalizations 54H11: Topological groups [See also 22A05]
Lin, Fucai; Xie, Li-Hong; Zhang, Jing. Direct limit topologies of quasi-uniform spaces and paratopological groups. Banach J. Math. Anal. 10 (2016), no. 1, 48--70. doi:10.1215/17358787-3163248. https://projecteuclid.org/euclid.bjma/1444913862