Conversation so far:
What is one-to-one correspondence?
He then began looking for a 1-to-1 correspondence between the points of the unit square and the points of a unit line segment.
What year was he doing his work on this?
In 1878, Cantor submitted another paper to Crelle's Journal, in which he defined precisely the concept of a 1-to-1 correspondence.
What is Crelle's Journal?
CANNOTANSWER.
How was his paper accepted?
This paper displeased Kronecker, and Cantor wanted to withdraw it.
Why did it displease Kronecker?
CANNOTANSWER.
Did he work with any other collegues during this time?
In an 1877 letter to Richard Dedekind, Cantor proved a far stronger result: for any positive integer n, there exists a 1-to-1 correspondence between the points.

Question: How did Dedekind accept this new result?
Self-contained rewrite: How did Dedekind accept Cantor's new result?