## Rocky Mountain Journal of Mathematics

### New Proofs of Bing's $\bf 1$-ULC Taming Theorem and Bing's Side Approximation Theorem

Davis W. Finley

#### Article information

Source
Rocky Mountain J. Math., Volume 23, Number 3 (1993), 885-897.

Dates
First available in Project Euclid: 5 June 2007

https://projecteuclid.org/euclid.rmjm/1181072530

Digital Object Identifier
doi:10.1216/rmjm/1181072530

Mathematical Reviews number (MathSciNet)
MR1245453

Zentralblatt MATH identifier
0816.57016

#### Citation

Finley, Davis W. New Proofs of Bing's $\bf 1$-ULC Taming Theorem and Bing's Side Approximation Theorem. Rocky Mountain J. Math. 23 (1993), no. 3, 885--897. doi:10.1216/rmjm/1181072530. https://projecteuclid.org/euclid.rmjm/1181072530

#### References

• J.W. Alexander, An example of a simply connected surface bounding a region which is not simply connected, Proc. Nat. Acad. Sci. U.S.A. 10 (1924), 6-8.
• --------, Remarks on a point set constructed by Antoine, Proc. Nat. Acad. Sci. U.S.A. 10 (1924), 10-12.
• Lois Antoine, Sur l'homeomorphie de deux figures et de leurs voisinages, J. Math. Pures Appl. 86 (1921), 221-325.
• R.H. Bing, Conditions under which a surface in $E^3$ is tame, Fund. Math. 47 (1959), 105-139.
• --------, A surface is tame if its complement is $1$-ULC, Trans. Amer. Math. Soc. 101 (1961), 294-305.
• --------, Approximating surfaces from the side, Ann. Math. 77 (1963), 145-192.
• M.G. Brin and T.L. Thickstun, On properly embedding noncompact surfaces in arbitrary 3-manifolds, Proc. London Math. Soc. 54 (1987), 350-366.
• E.M. Brown, M.S. Brown and C.D. Feustel, On properly embedding planes in $3$-manifolds, Proc. Amer. Math. Soc. 55 (1976), 461-464.
• E.M. Brown and C.D. Feustel, On properly embedding planes in arbitrary $3$-manifolds, Proc. Amer. Math. Soc. 94 (1985), 173-178.
• Morton Brown, A proof of the generalized Schoenflies theorem, Bull. Amer. Math. Soc. 66 (1960), 74-76.
• J.W. Cannon, ULC, properties in neighbourhoods of embedded surfaces and curves in $E^3$, Canad. J. Math. 25 (1973), 31-73.
• --------, New proofs of Bing's approximation theorems for surfaces, Pacific J. Math. 46 (1973), 361-379.
• James W. Cannon and Michael Starbird, A diagram oriented proof of Dehn's lemma, Topology Appl. 26 (1987), 193-205.
• W.T. Eaton, On $3$-manifolds $PL$-embedded in $S^4$ and the $PL$-Schoenflies theorem, preprint.
• --------, A generalization of the dog bone space to $E^n$, Proc. Amer. Math. Soc. 39 (1973), 379-387.
• --------, The sum of solid spheres, Michigan Math. J. 29 (1972), 193-207.
• Edwin E. Moise, Affine structures in $3$-manifolds. II. Positional properties of $2$-spheres, Ann. Math. 55 (1952), 172-176.
• C.D. Papakyriakopoulos, On Dehn's lemma and the asphericity of knots, Ann. Math. 62 (1957), 1-26.
• C.P. Rourke and B.J. Sanderson, Introduction to piecewise-linear topology, Springer-Verlag, Berlin, 1972.