Peter Cromwell's `Knots and Links' has a definition for a locally flat knot that I'm struggling to understand. It's more the terminology used rather than the concept (I hope) but I can't find a comparable formulation to help me. The part of the definition I'm struggling with is a follows:
"A point $p$ in a knot $K$ is locally flat if there exists some neighbourhood of $p$, call it $U$, such that the pair $(U, U\cap K)$ is homeomorphic to the unit ball $B_0(1)$, plus a diameter."
I simply don't understand the meaning of "plus a diameter", and I can't seem to find the phrase used in this context anywhere else. I (believe) I can visualise local flatness, and how it works in relation to knots, but I won't be confident as long as the crucial phrase remains a mystery to me!
Thanks in advance for any help.
Let $B$ be the unit ball in $R^3$ and let $X$ be the $x$-axis. What he means is that there be an homeomorphism of pairs between $(U,U\cap K)$ and $(B,B\cap X)$.