# Question about nowhere dense sets

## Main Question or Discussion Point

Suppose you know $k_0A$, for some set $A \subset X$ (where $X$ is a metric space) and some constant $k_0$, has nonempty interior. Do you then know that $A$ has nonempty interior, and/or that $k A$ has nonempty interior for any constant $k$?

HallsofIvy
Homework Helper
I don't know what you mean by "$k_0A$". Multiplication isn't defined in a general metric space.

I don't know what you mean by "$k_0A$". Multiplication isn't defined in a general metric space.
Point taken. Suppose we are in a vector space on which a metric has been defined.

Landau
Let A be subset of X, and k a non-zero scalar. Then $k\cdot\text{int}A=\text{int}kA$.