Articles written in Resonance – Journal of Science Education
Volume 27 Issue 1 January 2022 pp 131-142 Classroom
The Baire category theorem has numerous applications in real and functional analysis. In this note, we discuss an interesting application in the context of metric spaces. We characterize all subsets of a general metric space that appear as the set of continuity points for functions on that space. Furthermore, we juxtapose our results with the Tietze extension theorem, which beautifully leads us in another direction towards the study of extensions of continuous functions. Most of the results we discuss here already exist scattered in the literature. In this note, we strive to present them in a coherent form.
Volume 27 | Issue 9