  We show that if an Alexandrov space $X$ has an Alexandrov subspace $\bar
\Omega$ of the same dimension disjoint from the boundary of $X$, then the
topological boundary of $\bar \Omega$ coincides with its Alexandrov boundary.
Similarly, if a noncollapsed RCD(K,N) space $X$ has a noncollapsed RCD(K,N)
subspace $\bar \Omega$ disjoint from boundary of $X$ and with mild boundary
condition, then the topological boundary of $\bar \Omega$ coincides with its De
Philippis-Gigli boundary. We then discuss some consequences about convexity of
such type of equivalence.
