Pasting Lemma/Corollary 2
Jump to navigation
Jump to search
This theorem requires a proof..
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
 It has been suggested that this page or section be merged into Continuity from Union of Restrictions. (Discuss) |
Theorem
Let $X$ and $Y$ be topological spaces.
Let $\mathcal A = \left\{ {A_i: i \in I} \right\}$ be a set of sets that are open in $X$.
Let $f: \bigcup \mathcal A \to Y$ be a mapping such that:
- $\forall i \in I : f \restriction A_i$ is continuous
Then $f$ is continuous on $\bigcup \mathcal A$.
Proof
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
When this page/section has been completed, {{ProofWanted}} should be removed from the code.
If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page (see the proofread template for usage).
