# Digital topology

cragar

## Homework Statement

Show that the set of odd integers is dense in
the digital line topology on $\mathbb{Z}$

## The Attempt at a Solution

if m in Z is odd then it gets mapped to the set {m}=> open
.
So is the digital line topology just the integers.
If I was given any 2 integers I could find an odd one in between if there is an element in between.
If I was given to consecutive integers I wouldn't be able to find an odd one in between but there are no elements in between in this set. And I thinking about this question correctly.

Homework Helper
Can you spell out what the 'digital topology' is? {m} doesn't mean much to me.

cragar
I think I got it figured out. thanks for having me define my terms better.

Staff Emeritus
Homework Helper
Gold Member
FYI:

I Googled "digital line topology" and found the following:

For each $n\in\mathbb{Z}\,,$ de fine:
$\displaystyle \textit{B}(n) =\left\{\matrix{\{ n\},\ & \text{if }\ n \text{ is odd.} \\ \ \\ \{ n-1,\,n,\,n+1\}, & \text{if }\ n \text{ is even.}}\right.$
Consider $\displaystyle {\frak{B}}= \{B(n)|n\in\mathbb{Z}\}$: a (basis of the*) digital line topology.​