There is a smooth version of Urysohn’s Lemma which asserts the existence of a smooth function on smooth manifolds provided certain conditions are satisfied. The smooth version of Urysohn’s Lemma has similar conditions to the general Urysohn’s Lemma that holds on normal spaces and asserts the existence of a continuous function if the conditions of the Lemma are satisfied. Is there also a PL version of Urysohn’s Lemma? in other words is the following true :
Let $X$ be PL-manifold and let $A$ and $B$ be disjoint closed subsets. Then there exists a PL-function $f : X \longrightarrow [0, 1]$ such that $A \subset f^{−1}(0)$ and $B \subset f^{-1}(1)$.
? The smooth version can be found here :
http://www.math.ucla.edu/~petersen/manifolds.pdf Lemma 1.3.2
Remark : I asked this question on math-overflow and I was told it is not a research question so I am posting the question with more details here (since this place is aimed for questions that are not necessarily research-type questions).