Monotonically upper semicontinuity. (English) Zbl 1076.54010
Summary: We show that a function \(f\) from a topological vector space \(E\) into \(\mathbb{R}\) is uniformly continuous if and only if \(f\) is monotonically upper semicontinuous, a notion introduced by Y. Kimua, K. Tanaka and T. Tanaka. We also discuss similar conditions for monotonically upper semicontinuity.
MSC:
54C05 | Continuous maps |
54C30 | Real-valued functions in general topology |
46A99 | Topological linear spaces and related structures |