This is from Munkres, 2nd ed., Ch2, supp. exercise 7(a).
Definitions:
Topological Group:
is a topological group with identity
. This means that the product function
is continuous and
is a continuous map.
For
subsets of
.
.
Symmetric neighborhood: A neighborhood
of
such that
. Note that, for U open in G and
,
and
are both symmetric.
Claim: Any neighborhood U of e contains a symmetric neighborhood
such that
.
I can show that if V is symmetric, that
is an open set in
and
trivially. But I'm not seeing how to prove that a construction of a symmetric V from U has
?