Definition:Image of Topological Space

From ProofWiki
Jump to navigation Jump to search

Definition

Let $T = \left({S, \tau}\right)$ and $Q = \left({X, \tau'}\right)$ be topological spaces.

Let $f:S \to X$ be a mapping.


Then image (of the topological space $T$) of $f$ is equal to

$\operatorname{Im}\left({f}\right) := Q_{f\left[{S}\right]} = \left({f\left[{S}\right], \tau'_{f\left[{S}\right]} }\right)$

where $\tau'_{f\left[{S}\right]}$ denotes the subspace topology on $f\left[{S}\right]$.

Sources