Reference

A normal topological space, as referenced in Tietze's extension theorem, is a topological space that satisfies the T4 axiom. This means that for any two disjoint closed sets within the space, there exist disjoint open neighborhoods around each of the closed sets. According to the theorem, any real-valued continuous function defined on a closed subset of a normal topological space can be extended to a continuous function on the entire space. This property characterizes normal spaces and is fundamental in the study of topology, particularly in understanding the behavior of continuous functions and the structure of topological spaces. The theorem is widely used to prove various results in topology and related fields. For more detailed information, you can refer to sources like the Wikipedia page on Tietze's extension theorem.