A sufficient condition in terms of lower cut sets is given for the insertion of a continuous function between two comparable real-valued functions. The concept of a C-open set in a topological space ...

One confusing question over a long period of time is how transfer the discrete function transfers into continuous function. Recently the issue has been resolved but some details of the transformation ...

Teaching students to identify graphs of continuous functions is an important concept in mathematics. Understanding the continuity of a function can help students make predictions about the behavior of ...

Let F be a complete topological field. We undertake a study of the ring C(X, F) of all continuous F-valued functions on a topological space X whose topology is determined by C(X, F), in that it is the ...

Proceedings of the American Mathematical Society, Vol. 54, No. 1 (Jan., 1976), pp. 355-359 (5 pages) Let X and Y be topological spaces, let S be a dense subspace of X, and let f: S → Y be continuous.

Abstract: This paper mainly makes research on fractal dimension of fractal functions. We give basic estimation of fractal dimension, such as Box dimension and Hausdorff dimension, of fractional ...

National Clinical Research Center for Metabolic Diseases, Key Laboratory of Diabetes Immunology, Ministry of Education, Department of Metabolism and Endocrinology, The Second Xiangya Hospital of ...