Continuity for integers valued functions

Question

If $f:\mathbb{R}\to\mathbb{Z}$ is continuous, then $f$ is constant function.

Also: https://math.stackexchange.com/q/313904/42969, https://math.stackexchange.com/q/505472/42969 — Martin R, Feb 28 '19 at 06:39

little o · Answer 1 · 2019-02-28T06:41:56.207

0

Hint $:$ Continuous image of a connected set is connected. What are the connected subsets of $\Bbb Z$? Are they not the singletons?

edited Feb 28 '19 at 06:41

answered Feb 28 '19 at 06:36

little o

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