### Abstract

Original language | English |
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Publisher | Unknown Publisher |

Number of pages | 22 |

Volume | 1994-79 |

Publication status | Published - 1994 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 1994-79 |

### Fingerprint

### Keywords

- Optimization
- operations research

### Cite this

*Intersection theorems with a continuum of intersection points*. (CentER Discussion Paper; Vol. 1994-79). Unknown Publisher.

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**Intersection theorems with a continuum of intersection points.** / Herings, P.J.J.; Talman, A.J.J.

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - Intersection theorems with a continuum of intersection points

AU - Herings, P.J.J.

AU - Talman, A.J.J.

N1 - Pagination: 22

PY - 1994

Y1 - 1994

N2 - In all existing intersection theorems conditions are given under which acertain subset of acollection of sets has a non-empty intersection. In this paper conditions are formulated under which the intersection is a continuum of points satisfying some interesting topological properties. In this sense the intersection theorems considered in this paper belong to a new class. The intersection theorems are formulated on the unit cube and it is shown that both the vector of zeroes and the vector of ones lie in the same component of the intersection. This is interesting for some specific applications. The theorems give a generalization of the well-known lemmas of Knaster, Kuratowski, and Mazurkiewicz, of Sperner, of Shapley, and of Ichiischi. Moreover the results can be used to sharpen the usual formulation of the Sperner Lemma on the cube.

AB - In all existing intersection theorems conditions are given under which acertain subset of acollection of sets has a non-empty intersection. In this paper conditions are formulated under which the intersection is a continuum of points satisfying some interesting topological properties. In this sense the intersection theorems considered in this paper belong to a new class. The intersection theorems are formulated on the unit cube and it is shown that both the vector of zeroes and the vector of ones lie in the same component of the intersection. This is interesting for some specific applications. The theorems give a generalization of the well-known lemmas of Knaster, Kuratowski, and Mazurkiewicz, of Sperner, of Shapley, and of Ichiischi. Moreover the results can be used to sharpen the usual formulation of the Sperner Lemma on the cube.

KW - Optimization

KW - operations research

M3 - Discussion paper

VL - 1994-79

T3 - CentER Discussion Paper

BT - Intersection theorems with a continuum of intersection points

PB - Unknown Publisher

ER -