Question

If E is of nowheredense in R , then any subset of E is of nowhere dense In R​

Answer 1

Answer:

For example, Z is nowhere dense in R because it is its own closure, and it does not contain any open intervals (i.e. there is no (a,b) s.t. (a,b)⊂ˉZ=Z. An example of a set which is not dense, but which fails to be nowhere dense would be {x∈Q|0<x<1}. Its closure is [0,1], which contains the open interval (0,1).