Dear aspirant!

Hope you are doing well !

Proof of the theorem Is difficult to show here but here is the statement of the Theorem ;-

In topology, the Tietze extension theorem (also known as the Tietze–Urysohn–Brouwer extension theorem) states that continuous functions on a closed subset of a normal topological space can be extended to the entire space, preserving boundedness if necessary ..

Hope it helps you !

Thanks