$a)$What are the components and path components of $R_l$ ?
$b)$What are the continuous maps$ f : R → R_l$?
my attempt: i know that $ R_l$is totally disconnected....
2026-03-25 07:51:12.1774425072
Munkre topology Section 25 question 1
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Since you know that $\mathbb{R}_l$ is totally disconneted and since $\mathbb R$ is connected, then you now that the answer to (b) is: only the constant functions.
On the other hand, since $\mathbb{R}_l$ is totally disconnected, its only connected non-empty subsets are the singletons. And this implies that its only path-connected non-empty subsets are the singletons too.