Fundamental Definition and 947 Threads

Given a topological space and a group acting on it, the images of a single point under the group action form an orbit of the action. A fundamental domain or fundamental region is a subset of the space which contains exactly one point from each of these orbits. It serves as a geometric realization for the abstract set of representatives of the orbits.
There are many ways to choose a fundamental domain. Typically, a fundamental domain is required to be a connected subset with some restrictions on its boundary, for example, smooth or polyhedral. The images of a chosen fundamental domain under the group action then tile the space. One general construction of fundamental domains uses Voronoi cells.

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  1. Ben Wilson

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  2. mountains

    B Are there really 4 fundamental math operations?

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  3. S

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  4. jegues

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  5. TheSodesa

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  6. Vitani11

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  7. FallenApple

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  8. Charles Link

    Insights Fabry-Perot and Michelson Interferometry: A Fundamental Approach - Comments

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  9. C

    I Visual interpretation of Fundamental Theorem of Calculus

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  10. D

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  11. FallenApple

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  12. A

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  13. A

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  14. A

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  15. dkotschessaa

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  16. liometopum

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  17. Mayan Fung

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  18. Farhad70

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  19. M

    B The most fundamental "particle"

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  20. Mayan Fung

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  22. Z

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  23. M

    Fundamental Misunderstanding of SR…?

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  24. K

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  25. ManicPIxie

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  28. Math Amateur

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  29. Valour549

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  30. Eclair_de_XII

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  31. S

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  32. paulmdrdo

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  33. M

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  34. GhostLoveScore

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  35. Z

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  36. N

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  37. Z

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  38. R

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  39. faradayscat

    I Fundamental solutions and fundamental matrices

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  40. M

    A A fundamental question about research

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  41. N

    Need help with the 4 fundamental forces of Nature

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  42. 1

    A The fundamental group of preimage of covering map

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  43. M

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  44. M

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  45. S

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  46. F

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  47. S

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  48. tesselate

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  49. moriheru

    Foundations Proof of x^2n beeing even and other fundamental proofs

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  50. kostoglotov

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