ThmDex – An index of mathematical definitions, results, and conjectures.

Processing math: 100%

Result R2221 on D76: Set intersection

Set intersection is invariant under bijective shifting of indices

Formulation 0

Let

$X_j$ be a D11: Set for each

$j \in J$ .
Let

$\pi : J \to J$ be a D353: Set automorphism on

$J$ .

Then

$\begin{equation} \bigcap_{j \in J} X_j = \bigcap_{j \in J} X_{\pi(j)} \end{equation}$

Subresults

▶	R4215: Countable set intersection is invariant under bijective shifting of indices