Clarification on Notation in Munkres Topology

Question

I am reading Munkres Topology book and am trying to understand the proof of 83.1 (attached bellow) On the second line it says "for each alpha...", my question is what is alpha? A point? An arc? I'm a bit confused and I can't seem to find a part where he specified in the text. Is this a notational convention that I should be familiar with. For background, here is the only definition proceeding the lemma in this chapter:

Answer 1

Munkres's definition of a linear graph $X$ uses a given collection $A_\alpha$ of subspaces of $X$ with certain properties. As Matthias Klupsch comments, it is implicit here the indices $\alpha$ belong to some set $I$ (the index set). Perhaps is would have been better to say

... is a space $X$ that is written as the union of a collection $A_\alpha$, $\alpha \in I$, of subspaces ...

In the proof of Lemma 83.1 you should therefore understand

For each $\alpha \in I$ ...

or

For each edge of $X$ ...

An alternative definition could be this:

A linear graph is a space $X$ together with a set $\mathfrak A$ of subspaces of $X$, each of which is an arc, such that:

1. The intersection $A \cap A'$ of any two $A, A' \in \mathfrak A$ is either empty or consists of single point that is an end point of each.

2. The topology of $X$ is coherent with the subpaces $A \in \mathfrak A$.