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**Berger, Josef and Svindland, Gregor (2018): BROUWER'S FAN THEOREM AND CONVEXITY. In: Journal of Symbolic Logic, Vol. 83, No. 4: pp. 1363-1375**

**Full text not available from 'Open Access LMU'.**

## Abstract

In the framework of Bishop's constructive mathematics we introduce co-convexity as a property of subsets B of {0, 1}*, the set of finite binary sequences, and prove that co-convex bars are uniform. Moreover, we establish a canonical correspondence between detachable subsets B of {0, 1}* and uniformly continuous functions f defined on the unit interval such that B is a bar if and only if the corresponding function f is positive-valued, B is a uniform bar if and only if f has positive infimum, and B is co-convex if and only if f satisfies a weak convexity condition.

Item Type: | Journal article |
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Faculties: | Mathematics, Computer Science and Statistics > Mathematics |

Subjects: | 500 Science > 510 Mathematics |

ISSN: | 0022-4812 |

Language: | English |

Item ID: | 66381 |

Date Deposited: | 19. Jul 2019, 12:19 |

Last Modified: | 04. Nov 2020, 13:47 |