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 ...

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 ...

Abstract: Brouwer's continuity principle states that all functions from infinite sequences of naturals to naturals are continuous, that is, for every sequence the result depends only on a finite ...

We present old and new results about the size function of a set providing simple and complete proofs using basic tools of general topology. For instance, the decomposition of the size function is ...