Let $X \subset \mathbb{R}^n$ be a convex set. Now consider the statement
$$ x \in \mathrm{cl}(X)\; \backslash \; \mathrm{int}(X).$$
In this case, I am assured that there are two sequences, say $a_k \in \mathbb{R}^n \; \backslash \; \mathrm{cl}(X)$ and $b_k \in X$ such that $$\lim_{k\rightarrow \infty} a_k = \lim_{k\rightarrow \infty}b_k = x$$
Now consider $$ y \in \mathrm{cl}(X)\; \backslash \; \mathrm{relint}(X).$$ Here $\mathrm{relint}(X)$ is the interior with respect to the affine hull of $X$. In this case, is it correct to say that there again exist sequences say $c_k \in \mathbb{R}^n \; \backslash \; \mathrm{cl}(X)$ and $d_k \in X$ such that $$\lim_{k\rightarrow \infty} c_k = \lim_{k\rightarrow \infty}d_k = y$$