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 ...

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 ...

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 ...

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 ...

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 ...

Abstract: One of the most important properties of neural nets (NNs) for control purposes is the universal approximation property. Unfortunately,, this property is generally proven for continuous ...