Question

(a)Show that the digital line can be obtained as a quotient space that results
from a partition of R in the standard topology.
(b) Show that the digital plane, introduced in Section 1.4, can be obtained as a
quotient space that results from a partition of R2 in the standard topology.

Answer 1

b)

The digital plane has a basis defined as:

• are odd
• m even, n is odd
•    m odd, n is even
•   m,n are both even

The map to the integers with the digital line topology

  

is an open surjective map, thus a quotient map. Its square is thus an open quotient map as well.

a) based on same approach