Proving the union of two open sets is open

[Design]

Homework Statement

Prove if S₁ and S₂ are both open then S₁ $$\cap$$S₂ is also open

Homework Equations

S₁ is open means boundary(S₁) $$\subset$$ S_1^c

Same for S₂



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The Attempt at a Solution

We want to prove boundary(S₁$$\cap$$S₂) $$\subset$$ (S₁ (intersection) S₂)^c

Then idunno how to actually combine it.

 

[jbunniii]

The title says "union" of two open sets, but $\cap$ means intersection.

To get started, what is the definition of "boundary"? You need to relate the boundary of $S_1 \cap S_2$ to the boundaries of $S_1$ and $S_2$.