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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