# Six theorems about injective metric spaces

@article{Isbell1964SixTA,
title={Six theorems about injective metric spaces},
author={J. Isbell},
journal={Commentarii Mathematici Helvetici},
year={1964},
volume={39},
pages={65-76}
}
• J. Isbell
• Published 1964
• Mathematics
• Commentarii Mathematici Helvetici
340 Citations
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#### References

SHOWING 1-4 OF 4 REFERENCES