一句话：研究定义在左可计算实数边界区间上的可计算实函数何时能可计算延拓，并刻画其充要条件。
本文研究定义在区间上的可计算实函数，区间边界为左可计算实数（left-c.e. real），探讨该函数能否被可计算地延拓到边界。作者从数学分析、有效拓扑与经典可计算理论之间的联系出发，给出了可计算延拓的充要条件。结果表明，延拓可能性既取决于函数在边界附近的行为，也取决于边界所属的左可计算实数类，即该实数的构造方式。特别地，论文考察了一类由 c.e. 集合的可计算枚举构造的锯齿函数（sawtooth functions），说明边界构造信息在延拓问题中的作用。
We investigate interrelationships among different notions from mathematical analysis, effective topology, and classical computability theory. Our main object of study is the class of computable functions defined over an interval with the boundary being a left-c.e. real number. We investigate necessary and sufficient conditions under which such functions can be computably extended. It turns out that this depends on the behavior of the function near the boundary as well as on the class of left-c.e. real numbers to which the boundary belongs, that is, how it can be constructed. Of particular interest a class of functions is investigated: sawtooth functions constructed from computable enumerations of c.e. sets.