Continuous Functions on Open Intervals

This lecture covers the concept of continuous functions on open intervals, where a function is considered continuous if its restriction to the interval is also continuous. It also discusses the properties of the image of an open interval under a continuous function, highlighting that the image may not necessarily be open or bounded. Additionally, it explores the composition of two continuous functions and introduces elementary functions constructed from algebraic functions like exponentials, logarithms, and trigonometric functions. The lecture concludes by emphasizing the continuity of elementary functions on their domain of definition.