Definition:Image of Topological Space

Definition

Let $T = \struct {S, \tau}$ and $Q = \struct {X, \tau'}$ be topological spaces.

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

The image (of the topological space $T$) of $f$ is defined as:

$\Img f := Q_{f \sqbrk S} = \struct {f \sqbrk S, \tau'_{f \sqbrk S} }$

where $\tau'_{f \sqbrk S}$ denotes the subspace topology on $f \sqbrk S$.

Sources

• Mizar article WAYBEL18:def 6