Category:Isometry Preserves Sequence Convergence
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This category contains pages concerning Isometry Preserves Sequence Convergence:
Let $M_1 = \struct {S_1, d_1}$ and $M_2 = \struct {S_2, d_2}$ both be metric spaces or pseudometric spaces.
Let $\phi: S_1 \to S_2$ be an isometry.
Let $\sequence {x_n}$ be an infinite sequence in $S_1$.
Suppose that $\sequence {x_n}$ converges to a point $p \in S_1$.
Then $\sequence {\map \phi {x_n}}$ converges to $\map \phi p$.
Pages in category "Isometry Preserves Sequence Convergence"
The following 3 pages are in this category, out of 3 total.