Title of the talk: Continuous Functions on Metric Spaces Date: 16th February 2025 Time: 3 PM Zoom Meeting ID: 890 5084 4173 Passcode: 161489 Abstract: We will discuss basic properties of Cauchy continuous functions. As an application of the Tietze extension theorem, we will characterize metric spaces in which every continuous function is necessarily Cauchy continuous. Additionally, we will show that if is a non-empty subset of a metric space and is Cauchy continuous, then has a Cauchy continuous extension to the metric space. Hoping to see you in the talk!!