I'm reading the proof for Tietze Extension Theorem from Munkres 2nd. Edition, Section 35, it's $\textbf{Theorem 35.1}$. Part $(a)$ is ok but i'm having trouble understanding the second implication, $(b)$.
$f$ is a continuous map $f:A\to (-1,1)$, we can extend it to $g:X\to [-1,1]$. We now want to find a function $h$ such that $h:X\to (-1,1)$.
Then, we have $\phi:X\to[0,1]$ such that $\phi(D)=\{0\},~\phi(A)=\{1\}$ and define $$h(x)=\phi(x)g(x).$$
$h$ is continuous since it's the product of continuous functions, and here is where I get stuck:
$$h(a)=\phi(a)g(a)=1\Delta g(a)=f(a)$$ if $a\in A$ and $$h(x)=0\Delta g(x)=0$$ if $x\in D$.
What does $\Delta$ mean? I've read almost all sections from 10 to 43, and never seen it. The only thing I know is $\Delta$ is the diagonal of a product space $X\times X$ but it has no sense here.
Edit 1: Maybe it's a product between de functions, that is not necessarily the usual one?
Edit 2: $\textbf{Theorem 36.2}$ explains $\Delta$ is a kind of product.
As someone has noted in the comments, $\Delta$ does not appear in the English versions of Munkres. However, in the Spanish version of Munkres 2nd Edition, one does find $\Delta$! Comparing the two texts, I suspect $\Delta$ is used in place of $\cdot$ to denote multiplication.
For example, the corresponding sections in Theorem 35.1 are $h(x) = 0 \cdot g(x) = 0$ in the English version, and $h(x) = 0\Delta g(x) = 0$ in the Spanish version. As additional evidence, the English version of Theorem 36.2 has $h_{i}(x) = \phi_{i}(x) \cdot g_{i}(x)$ as part of a piecewise definition, whereas the Spanish version has $\phi_{i}(x)\Delta g_{i}(x).$