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集合・位相入門/松坂和夫 5.2 節:コンパクト性

集合・位相入門/松坂和夫 5.2 節:コンパクト性

阪大の学生で開催した『位相・集合・多様体勉強会』の発表スライドです.『集合・位相入門/松坂和夫』の 5.2 節:コンパクト性を取り扱っています.

NomotoEriko

April 25, 2019
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  17. $  Hausdroff #( <&> "#( ! "!  2

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  18. Hausdroff     !" <> #, % 

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  20. #&%"$2  Hausdroff :E 08 14 Hausdroff :E ! B+G,

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  21. #&%"$2  Hausdroff :E 08 14 Hausdroff :E ! B+G,

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  22. #  Hausdroff '- !& 14 Hausdroff '- ! *.

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  23. * Hausdroff 19 (. 14 Hausdroff 19 ! 7%:' "

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  25. !"% !"  $& <!" $& #  > #

     !"  $(&; ()  ( #  ) '& ! $&  #
  26. 019 !"   6:" $. 16 Euclid 19 !"

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  27. +,7 !"   4!8# %) 16 Euclid ,7 !"

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  28. -.4 !"   2#6% &+ 16 Euclid .4 !"

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  29. (). !"   ,/! "& 16 Euclid ). !"

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  30. !" 16 Euclid !" # # !" ] < [

    > # ] ⇒ # # !" ] # !" ] % = '( , *( × ⋯×['" , *" ] % [ 11 M ! ] [', *] [ 13 J [ ! ] / = [', *] [ 11 0 0 ] # 13 (Tychonoff) (02 )2∈5 0 = ∏ 2∈5 02 0 7 ∈ Λ 02
  31. !" 16 Euclid !" # [ # !" < >

    # ⇒ # % & = [), +] ! [ - ∈ & [ % [), -] [ % [), -] & - &/ ) + %
  32. !" 16 Euclid !" # [ # !" < >

    # ⇒ # % & = [), +] ! [ - ∈ & [ % [), -] [ % [), -] & - &/ ) + % - &/ % %
  33. [ !" ] 16 Euclid [ !" ] # #

    !" ] < > # ] ⇒ # % & = [), +] ! - ∈ & % [), -] % [), -] & - ] &/ + ∈ &/ ! [ & = [), +] ) + % - % &/
  34. !" 16 Euclid !" # # !" [ < >

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  35. !" 16 Euclid !" # # !" [ < >

    # ⇒ # % − ' ∈ )* [,, % − '] / 01 , ⋯ , 03 [ ,, % − ' ∪ % − ', % + ' = [,, % + '] 01 , ⋯ , 03 , 0 [ % ∈ )*[ % < 8 % + ' ∈ )* ' % )* [ % = 8, 8 ∈ )* 8 0 )* % % − ' % + '
  36. !" 16 Euclid !" # # !" [ < >

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  37. ./4 !"  2"5% ', 16 Euclid /4 !" 2"5%

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  38. !   ;$?& *3 16 Euclid 6= !" ;$?&

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  39. !  !$# " J*N, 2? 16 Euclid BL !"

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  40. %)  06 <"2> 3 9/06 ! (- # 

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  41. .GHQ" %('$& HQ 7N :F 17 ! = (S, &)

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