When I took a first course in differential topology, I remember reading a blog post(?) that made a comment along the lines of
Surjectivity is injectivity, but one dimension higher.
The content of this statement was that to prove a map $f:M\to N$ was surjective, we could prove that a related map $F:M\times I\to N$ was injective instead, and this would imply surjectivity of $f$. I'm looking to see if anyone knows of the source of this quote, or could explain its content in greater detail.
from Hot Weekly Questions - Mathematics Stack Exchange
Post a Comment