### Function and colorful extensions of the KKM theorem

#### Abstract

#### Keywords

#### References

I. Baraný, A generalization of Carathéodory’s theorem, Discrete Math. 40 (1982), 141–152.

H. Ben-El-Mechaiekh, S. Chebbi, M. Florenzano and J. Llinares, Abstract convexity and fixed points, J. Math. Anal. Applications 222 (1998), 138–150.

J. De Loera, X. Goaoc, F. Meunier and N. Mustafa, The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg, Bull. Amer. Math. (N.S.) 56 (2019), no. 3, 415–511.

G. Demange, D. Gale and M. Sotomayor, Multi-item auctions, Journal of Political Economy 94 (1986), 863– 872.

B. Fain, K. Munagala and N. Shah, Fair Allocation of Indivisible Public Goods, ArXiv 805-03, May 2018.

Y. (Kobi) Gal, M. Mash, A. Procaccia and Z. Zick, Which is the fairest (rent division) of them all? Journal of the ACM, Vol. 64, No. 6, Article 39, publication date: November 2017.

D. Gale, Equilibrium in a discrete exchange economy with money, Internat. J. Game Theory 13 (1983), no. 1, 61–64.

A. Granas, KKM-Maps, The Scottish Book; Mathematics from the Scottish Café with Selected Problems from the New Scottish Book (R. Mauldinm, ed.), 2nd edition, Birkhäuser, 2015; Chapter 5, pp. 34–48.

A. Idzik, W. Kulpa and P. Mackowiak, Equivalent forms of the Brouwer fixed point theorem I, Topol. Methods Nonlinear Anal. 44 (2014), no. 1, 263–276.

G. Kalai and R. Meshulam, A topological colorful Helly theorem, Adv. Math. 191 (2005), 305–311.

B. Knaster, K. Kuratowski and S. Mazurkiewicz, Ein Beweis des Fixpunktsatzes für n-dimensionale Simplexe, Fund. Math. 14 (1929), 132–137. (in German)

W. Kulpa, Convexity and the Brouwer Fixed Point Theorem, Topology Proc. 22 (1997), 211–235.

K. Kuratowski, Introduction to Set Theory and Topology, International Series of Monographs in Pure and Applied Mathematics, revised second English ed., Number 101, Pergamon Press, WArsaw, 1972.

J. Matoušek, Lectures on Discrete Geometry, Springer–Verlag New York, Inc., 2002.

S. Park, New generalizations of basic theorems in the KKM theory, Nonlinear Anal. 74 (2011), 300–310.

S. Park, One hundred years of Brouwer’s fixed point theorem, circulated notes.

S. Park, A History of the KKM Theory, https://www.researchgate.net/publication/324388798.

L.-G. Svensson, Large indivisibles: An analysis with respect to price equilibrium and fairness, Econometrica 51 (1983), no. 4, 939–954.

### Refbacks

- There are currently no refbacks.