Is Munkres Lemma 81.1 Misinterpreted Regarding Normal Subgroups?

[ehrenfest]

[SOLVED] munkres lemma 81.1

Homework Statement

Please stop reading this if you do not have Munkres.

The statement of this lemma implies that pi_1(B,b_0)/H_0 is a group. That does not make sense to me because H_0 is not necessarily normal in pi_1(B,b_0).

Homework Equations

The Attempt at a Solution

 

[masnevets]

Replace the word subgroup with subset and the statement becomes less confusing. Munkres is only talking about \pi_1(B, b_0) / H_0 as a set of cosets.