The Kline 2-sphere characterization—by definition

The Kline 2-sphere characterization—by definition
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Proc. Amer. Math. Soc. 48 (1975), 491-498

DOI: https://doi.org/10.1090/S0002-9939-1975-0358780-5

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Brick partitionings are used repeatedly to prove, by definition, the classical Kline $2$-sphere characterization.

References

R. H. Bing, The Kline sphere characterization problem, Bull. Amer. Math. Soc. 52 (1946), 644–653. MR 16645, DOI 10.1090/S0002-9904-1946-08614-0
R. H. Bing, Partitioning a set, Bull. Amer. Math. Soc. 55 (1949), 1101–1110. MR 35429, DOI 10.1090/S0002-9904-1949-09334-5
R. H. Bing, Complementary domains of continuous curves, Fund. Math. 36 (1949), 303–318. MR 38063, DOI 10.4064/fm-36-1-303-318
Richard Slocum, Using brick partitionings to establish conditions which insure that a Peano continuum is a $2$-cell, a $2$-sphere or an annulus, Pacific J. Math. 42 (1972), 763–775. MR 321036
Raymond Louis Wilder, Topology of Manifolds, American Mathematical Society Colloquium Publications, Vol. 32, American Mathematical Society, New York, N. Y., 1949. MR 0029491
Gail S. Young Jr., A characterization of $2$-manifolds, Duke Math. J. 14 (1947), 979–990. MR 23061

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