Inverse Mapping is Bijection
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Let $S$ and $T$ be sets.
Let $f: S \to T$ and $g: T \to S$ be inverse mappings of each other.
Then $f$ and $g$ are bijections.
The result follows by definition of bijection.
- 1965: Claude Berge and A. Ghouila-Houri: Programming, Games and Transportation Networks ... (previous) ... (next): $1$. Preliminary ideas; sets, vector spaces: $1.1$. Sets
- 1975: Bert Mendelson: Introduction to Topology (3rd ed.) ... (previous) ... (next): Chapter $1$: Theory of Sets: $\S 9$: Inverse Functions, Extensions, and Restrictions