Category:Final Topology

This category contains results about the final topology.
Definitions specific to this category can be found in Definitions/Final Topology.

Let $X$ be a set.

Let $I$ be an indexing set.

Let $\family {\struct{Y_i, \tau_i}}_{i \mathop \in I}$ be an $I$-indexed family of topological spaces.

Let $\family {f_i: Y_i \to X}_{i \mathop \in I}$ be an $I$-indexed family of mappings.

Definition 1

The final topology on $X$ with respect to $\family {f_i}_{i \mathop \in I}$ is defined as:

$\tau = \set{U \subseteq X: \forall i \in I: \map {f_i^{-1}} U \in \tau_i} \subseteq \powerset X$