# Topology — Shape without Measurement

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Category: Mathematics
Slides: 13
Updated: 2026-05-15T22:19:42.374Z
Tags: catalog, math, topology

## Summary

homeomorphism Same shape, different presentation. The puzzle To a topologist, a coffee cup is a donut. Stretch, bend, twist — but never cut, never glue. Under such deformations the cup with one handle and the torus with one hole are indistinguishable. Both are surfaces of genus one. Key sections include: TOPOLOGY / Shape without measurement; To a topologist, a coffee cup is a donut.; Euler and the seven bridges of Königsberg.; Topology studies properties preserved under continuous deformation.; A topological space is a set with a chosen family of open sets.; Euler characteristic.; The Möbius strip : one side, one edge.; The Klein bottle : a surface with no inside.; Closed loops in space, classified up to ambient isotopy.; Translate shapes into groups..

## Slide Outline

1. TOPOLOGY / Shape without measurement
2. To a topologist, a coffee cup is a donut.
3. Euler and the seven bridges of Königsberg.
4. Topology studies properties preserved under continuous deformation.
5. A topological space is a set with a chosen family of open sets.
6. Euler characteristic.
7. The Möbius strip : one side, one edge.
8. The Klein bottle : a surface with no inside.
9. Closed loops in space, classified up to ambient isotopy.
10. Translate shapes into groups.
11. Poincaré, 1904. Perelman, 2003.
12. From the abstract to the tangible.
13. Continue.

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