### Abstract

The great achievement of Cantor and Dedekind in the 19th c. was not the arithmetization of the geometrical line, but rather the use of the notion of set to extend the number system to the reals and the transfinite numbers, and to recast the line as a set of points and numbers systems as sets of numbers: this prepares the ground for the emergence of topology and then algebraic topology in the 20th c. and the novel diagrams that accompany its presentation in the textbook written by Singer and Thorpe.

Original language | English (US) |
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Title of host publication | Diagrammatic Representation and Inference - 10th International Conference, Diagrams 2018, Proceedings |

Editors | Gem Stapleton, Francesco Bellucci, Amirouche Moktefi, Peter Chapman, Sarah Perez-Kriz |

Publisher | Springer Verlag |

Pages | 814-816 |

Number of pages | 3 |

ISBN (Print) | 9783319913759 |

State | Published - Jan 1 2018 |

Event | 10th International Conference on the Theory and Application of Diagrams, Diagrams 2018 - Edinburgh, United Kingdom Duration: Jun 18 2018 → Jun 22 2018 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10871 LNAI |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 10th International Conference on the Theory and Application of Diagrams, Diagrams 2018 |
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Country | United Kingdom |

City | Edinburgh |

Period | 6/18/18 → 6/22/18 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Diagrammatic Representation and Inference - 10th International Conference, Diagrams 2018, Proceedings*(pp. 814-816). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10871 LNAI). Springer Verlag.

}

*Diagrammatic Representation and Inference - 10th International Conference, Diagrams 2018, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10871 LNAI, Springer Verlag, pp. 814-816, 10th International Conference on the Theory and Application of Diagrams, Diagrams 2018 , Edinburgh, United Kingdom, 6/18/18.

**The central role of diagrams in algebraic topology.** / Grosholz, Emily R.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - The central role of diagrams in algebraic topology

AU - Grosholz, Emily R.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - The great achievement of Cantor and Dedekind in the 19th c. was not the arithmetization of the geometrical line, but rather the use of the notion of set to extend the number system to the reals and the transfinite numbers, and to recast the line as a set of points and numbers systems as sets of numbers: this prepares the ground for the emergence of topology and then algebraic topology in the 20th c. and the novel diagrams that accompany its presentation in the textbook written by Singer and Thorpe.

AB - The great achievement of Cantor and Dedekind in the 19th c. was not the arithmetization of the geometrical line, but rather the use of the notion of set to extend the number system to the reals and the transfinite numbers, and to recast the line as a set of points and numbers systems as sets of numbers: this prepares the ground for the emergence of topology and then algebraic topology in the 20th c. and the novel diagrams that accompany its presentation in the textbook written by Singer and Thorpe.

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UR - http://www.scopus.com/inward/citedby.url?scp=85048636503&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85048636503

SN - 9783319913759

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 814

EP - 816

BT - Diagrammatic Representation and Inference - 10th International Conference, Diagrams 2018, Proceedings

A2 - Stapleton, Gem

A2 - Bellucci, Francesco

A2 - Moktefi, Amirouche

A2 - Chapman, Peter

A2 - Perez-Kriz, Sarah

PB - Springer Verlag

ER -