TOPOLOGY OF QUASI-PSEUDOMETRIC SPACES AND CONTINUOUS LINEAR OPERATOR ON ASYMMETRIC NORMED SPACES

. In this paper, we will discuss about topological properties of quasi-pseudometric spaces and properties of linear operators in asymmetric normed spaces. The topological properties of quasi-pseudometric spaces will be given consisting of open and closed set properties in quasi-pseudometric spaces. The discussion about properties of linear operator on asymmetric normed spaces is focus on the uniform boundedness principle. The uniform boundedness theorem is proved by utilizing completeness properties and characteristic of closed sets on quasi-pseudometric spaces.