Continuity theorems for a class of computable operators

Computable operators corresponding to the concept of a left computably enumerable real number, called \textit{$\mathrm{L}$-operators}, are studied. Their continuity properties most commonly used in the constructive mathematical analysis of A. A. Markov's school are examined. It is proved that any $\mathrm{L}$-operator is nondecreasing and almost left continuous. An example of an $\mathrm{L}$-operator which is neither left continuous nor right pseudocontinuous at some point is constructed. An almost continuity criterion for an $\mathrm{L}$-operator is found. This criterion is used to prove that almost continuous $\mathrm{L}$-operators are not necessarily continuous or pseudouniformly continuous on a closed interval.