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There are two complete metric spaces $(A,d_A)$ and $(B,d_B)$, also $B \subset A$, so there is a third induced metric space $(B,d_A)$. There is a continuous and onto function $e:A\to B$. For any $b \in B$, let $P(b)$ denote the set of all punctured neighbourhoods of $b$ in the metric space $(B,d_B)$.

For every $b \in B$, any $a \in e^{-1}(\{b\})$ is a limit point of every set in $P(b)$ under the metric $d_A$.

Is there a compact notation/notion/definition for the above setup?

PS : $e^{-1}(\{b\})$ is the pre-image of the element $b \in B$

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  • $\begingroup$ Is this some type of embedding? $\endgroup$ – Rajesh Dachiraju Jul 29 '18 at 1:27

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