Homeomorphic continuous curves in 2-space are isotopic in 3-space.

Homeomorphic continuous curves in $2$-space are isotopic in $3$-space.
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by W. K. Mason

Trans. Amer. Math. Soc. 142 (1969), 269-290

DOI: https://doi.org/10.1090/S0002-9947-1969-0246276-2

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References

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Concerning the common boundary of two domains

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Gordon Thomas Whyburn, Analytic Topology, American Mathematical Society Colloquium Publications, Vol. 28, American Mathematical Society, New York, 1942. MR 0007095, DOI 10.1090/coll/028

Concerning continuous curves

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Summary of lectures and Seminars, Summer Institute on Set Theoretic Topology