1. notice
  2. ไธญๆ–‡
  3. 1. feature
  4. ้€ป่พ‘
  5. 2. ้€ป่พ‘
  6. 3. ้›†ๅˆ่ฎบ
  7. 4. ๆ˜ ๅฐ„
  8. 5. ๅบ
  9. 6. ็ป„ๅˆ
  10. ๅพฎ็งฏๅˆ†
  11. 7. ๅฎžๆ•ฐ
  12. 8. ๆ•ฐๅˆ—ๆž้™
  13. 9. โ„^n
  14. 10. Euclidean ็ฉบ้—ด
  15. 11. Minkowski ็ฉบ้—ด
  16. 12. ๅคš้กนๅผ
  17. 13. ่งฃๆž (Euclidean)
  18. 14. ่งฃๆž (Minkowski)
  19. 15. ่งฃๆž struct ็š„ๆ“ไฝœ
  20. 16. ๅธธๅพฎๅˆ†ๆ–น็จ‹
  21. 17. ไฝ“็งฏ
  22. 18. ็งฏๅˆ†
  23. 19. ๆ•ฃๅบฆ
  24. 20. ็ฝ‘ๆž้™
  25. 21. ็ดง่‡ด
  26. 22. ่ฟž้€š
  27. 23. ๆ‹“ๆ‰‘ struct ็š„ๆ“ไฝœ
  28. 24. ๆŒ‡ๆ•ฐๅ‡ฝๆ•ฐ
  29. 25. ่ง’ๅบฆ
  30. ๅ‡ ไฝ•
  31. 26. ๆตๅฝข
  32. 27. ๅบฆ่ง„
  33. 28. ๅบฆ่ง„็š„่”็ปœ
  34. 29. Levi-Civita ๅฏผๆ•ฐ
  35. 30. ๅบฆ่ง„็š„ๆ›ฒ็އ
  36. 31. Einstein ๅบฆ่ง„
  37. 32. ๅธธๆˆช้ขๆ›ฒ็އ
  38. 33. simple-symmetric-space
  39. 34. ไธปไธ›
  40. 35. ็พคไฝœ็”จ
  41. 36. ็ƒๆžๆŠ•ๅฝฑ
  42. 37. Hopf ไธ›
  43. ๅœบ่ฎบ
  44. 38. ้ž็›ธๅฏน่ฎบ็‚น็ฒ’ๅญ
  45. 39. ็›ธๅฏน่ฎบ็‚น็ฒ’ๅญ
  46. 40. ็บฏ้‡ๅœบ
  47. 41. ็บฏ้‡ๅœบ็š„ๅฎˆๆ’ๆต
  48. 42. ้ž็›ธๅฏน่ฎบ็บฏ้‡ๅœบ
  49. 43. ๅ…‰้”ฅๅฐ„ๅฝฑ
  50. 44. ๆ—ถ็ฉบๅŠจ้‡็š„่‡ชๆ—‹่กจ็คบ
  51. 45. Lorentz ็พค
  52. 46. ๆ—‹้‡ๅœบ
  53. 47. ๆ—‹้‡ๅœบ็š„ๅฎˆๆ’ๆต
  54. 48. ็”ต็ฃๅœบ
  55. 49. ๅผ ้‡ๅœบ็š„ Laplacian
  56. 50. Einstein ๅบฆ่ง„
  57. 51. ็›ธไบ’ไฝœ็”จ
  58. 52. ่ฐๆŒฏๅญ้‡ๅญๅŒ–
  59. 53. ๆ—‹้‡ๅœบๆ‚้กน
  60. 54. ๅ‚่€ƒ
  61. English
  62. 55. notice
  63. 56. feature
  64. logic-topic
  65. 57. logic
  66. 58. set-theory
  67. 59. map
  68. 60. order
  69. 61. combinatorics
  70. calculus
  71. 62. real-numbers
  72. 63. limit-sequence
  73. 64. โ„^n
  74. 65. Euclidean-space
  75. 66. Minkowski-space
  76. 67. polynomial
  77. 68. analytic-Euclidean
  78. 69. analytic-Minkowski
  79. 70. analytic-struct-operation
  80. 71. ordinary-differential-equation
  81. 72. volume
  82. 73. integral
  83. 74. divergence
  84. 75. limit-net
  85. 76. compact
  86. 77. connected
  87. 78. topology-struct-operation
  88. 79. exponential
  89. 80. angle
  90. geometry
  91. 81. manifold
  92. 82. metric
  93. 83. metric-connection
  94. 84. geodesic-derivative
  95. 85. curvature-of-metric
  96. 86. Einstein-metric
  97. 87. constant-sectional-curvature
  98. 88. simple-symmetric-space
  99. 89. principal-bundle
  100. 90. group-action
  101. 91. stereographic-projection
  102. 92. Hopf-bundle
  103. field-theory
  104. 93. point-particle-non-relativity
  105. 94. point-particle-relativity
  106. 95. scalar-field
  107. 96. scalar-field-current
  108. 97. scalar-field-non-relativity
  109. 98. projective-lightcone
  110. 99. spacetime-momentum-spinor-representation
  111. 100. Lorentz-group
  112. 101. spinor-field
  113. 102. spinor-field-current
  114. 103. electromagnetic-field
  115. 104. Laplacian-of-tensor-field
  116. 105. Einstein-metric
  117. 106. interaction
  118. 107. harmonic-oscillator-quantization
  119. 108. spinor-field-misc
  120. 109. reference

note-math

[net]

a net of := (a collection of subset of ) with property

  • (ๅซไน‰: ๆ”ถๆ•›ๅˆฐๆž้™ไน‹ๅ‰้ž็ฉบ. ๅฆ‚ๆžœ ๅ…ƒ็ด ๆ— ้™้‚ฃไนˆๆœ‰้™ไบค้›†ๆŽงๅˆถ็€ๆ”ถๆ•›ๆ–นๅ‘, ๅฐฝ็ฎกๅฏ่ƒฝ . ๅฆ‚ๆžœ ๅ…ƒ็ด ๆœ‰้™้‚ฃไนˆ )

Example , ็ฝ‘

็‚น็ฝ‘ or ๅŒ…ๅซ็‚น ็š„็ฝ‘

็ฝ‘ ็ป†ไบŽ :=
ๅนถไธ”่ฟ™่•ดๅซ

[net-same-limit] ๆž้™็›ธๅŒ := ็›ธไบ’็ป†ไบŽ

ๅนถไธๆ˜ฏๆ‰€ๆœ‰ๆž้™็›ธๅŒ็š„็ฝ‘้ƒฝๆœ‰็”จ. ้›†ๅˆ่ฎบไธŠๅฏ็”จ ๆž„้€ ๅ‡บๆ–ฐ็š„ๆž้™็›ธๅŒ็š„็ฝ‘, ไฝ†ๆœ‰ๅพˆๅคšๅ†—ไฝ™

ไปปไฝ•็ฝ‘้ƒฝๅฏไปฅ่กฅๅ……ๆ‰€ๆœ‰็š„ๆœ‰้™ไบค้›† ๆˆไธบๆ–ฐ็š„็ฝ‘, ๅนถไฟๆŒ็›ธๅŒ็š„ๆž้™

[hom-limit] ็ฝ‘ไน‹้—ด็š„ๆž้™ๅŒๆ€ :=

. ็ฝ‘ ็ป†ไบŽ

็”จ็‚นๆฅๆ่ฟฐๅฐฑๆ˜ฏ

Example

  • ๅบๅˆ— ๆ”ถๆ•›

ไฝฟ็”จๅŒ…ๅซ ็š„ๆ‰€ๆœ‰ๅŒบ้—ด ๅ’Œ , ๅˆ™ ๆž้™ๅŒๆ€

  • ๅ‡ฝๆ•ฐๆž้™

let , ไปŽ ๅˆฐ