Mod 2 degree and a generalized no retraction theorem. (English) Zbl 1089.55001
Summary: We provide elementary proofs of generalized versions of the No Retraction Theorem and Sperner’s Lemma, and a simple definition of mod 2 degree of certain maps.
MSC:
| 55M20 | Fixed points and coincidences in algebraic topology |
| 55M25 | Degree, winding number |
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
References:
| [1] | Brown, Proc. Natl. Acad. Sci. USA 47 pp 113– (1961) |
| [2] | Bing, Amer. Math. Monthly 76 pp 119– (1969) |
| [3] | Fan, Ann. New York Acad. Sci. 31 pp 125– (1970) · Zbl 0227.57006 · doi:10.1111/j.1749-6632.1970.tb56463.x |
| [4] | Freund, J. Combin. Theory Ser. B 47 pp 192– (1989) |
| [5] | Graph Theory (Addison-Wesley, Reading, MA, 1969). |
| [6] | Hirsch, Proc. Amer. Math. Soc. 14 pp 364– (1963) |
| [7] | Joshi, Proc. Amer. Math. Soc. 128 pp 1523– (2000) |
| [8] | Milnor, Amer. Math. Monthly 85 pp 521– (1978) |
| [9] | Rogers, Amer. Math. Monthly 87 pp 525– (1980) |
| [10] | Sanderson, Topology Proc. 1 pp 79– (1976) |
| [11] | Shashkin, Publ. Math. Debrecen 45 pp 407– (1994) |
| [12] | Shashkin, Publ. Math. Debrecen 49 pp 301– (1996) |
| [13] | Sieklucki, Comment. Math. Prace Mat. 23 pp 129– (1983) |
| [14] | Sies, Fund. Math. 118 pp 135– (1983) |
| [15] | Algebraic Topology (McGraw-Hill, New York, 1966). |
| [16] | On Sperner’s lemma and another combinatorial lemma, Proceedings of the Second International Conference on Combinatorial Mathematics, New York, 1978, Annals of the New York Academy of Sciences Vol. 319 (New York Acad. Sci., New York, 1979), pp. 536–539. |
| [17] | Zeeman, Math. Proc. Cambridge Philos. Soc. 60 pp 39– (1964) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
