Compactness and the Finite Intersection Property

Поділитися
Вставка
  • Опубліковано 11 січ 2025

КОМЕНТАРІ • 32

  • @alishermirmanov5608
    @alishermirmanov5608 8 місяців тому

    Great Video Sir! Amazing video with clear explanation,

  • @ErendiraCabrera-x6u
    @ErendiraCabrera-x6u 2 місяці тому

    Clear explanation!!!

  • @thomasqiao916
    @thomasqiao916 6 років тому

    Thank you so much for this video! I've looked so long for a channel that explains topology this well.

    • @Squiralnuts
      @Squiralnuts 4 роки тому

      wrong concept you providing us
      How you can say that if intersection of infinite no sets is empty how you say that the family of same sets with finite intersection also empty. For easy example let A1={2,3,4} A2={3,4,5} and A3={5,6} then intersection of A1, A2, A3 is empty, but intersection of A1, A2 ={3,4} and A2, A3={5}.
      You are wrong pls read and then teach us

    • @blenderstuff7861
      @blenderstuff7861 4 роки тому

      @Infinity Chess , shut up noob. Watch whole video carefully and then try to understand. Sometimes we judges someone incorrectly due to our less understanding of things. Don't judge him, he taught that correctly.

  • @vishwakarmasharama3237
    @vishwakarmasharama3237 5 років тому

    Aapke jaisa koi topology kar finite intersection property nahi padha sakta ta hai very good

    • @Squiralnuts
      @Squiralnuts 4 роки тому

      wrong concept you providing us
      How you can say that if intersection of infinite no sets is empty how you say that the family of same sets with finite intersection also empty. For easy example let A1={2,3,4} A2={3,4,5} and A3={5,6} then intersection of A1, A2, A3 is empty, but intersection of A1, A2 ={3,4} and A2, A3={5}.
      You are wrong pls read and then teach us

    • @Squiralnuts
      @Squiralnuts 4 роки тому

      he was wrong F.I.P. fails how u can say X compact

    • @Squiralnuts
      @Squiralnuts 4 роки тому

      watch npTEL topology videos

    • @blenderstuff7861
      @blenderstuff7861 4 роки тому

      @@Squiralnuts , shut up noob. Watch whole video carefully and then try to understand. Sometimes we judges someone incorrectly due to our less understanding of things. Don't judge him, he taught that correctly.

  • @blenderstuff7861
    @blenderstuff7861 4 роки тому

    Great explanation sir

  • @henrytian8612
    @henrytian8612 4 роки тому +1

    The contrapositive of P -> Q is NotQ -> NotP.
    So isn't the contrapositive in the forward direction: Given any family of sets without FIP and intersection of the entire family is empty, then that implies X is not compact?
    Seems like the theorem being proved is that:
    A finite collection of closed subsets F have nonempty intersection the intersection of all closed subsets of F have nonempty intersection? So seems like the arrow is in the wrong place on the board?

  • @aboyhya612
    @aboyhya612 2 роки тому

    Obvious proof. Thank you mester

  • @wesleyrm
    @wesleyrm Рік тому

    Thank you!

  • @muskangoel6292
    @muskangoel6292 5 років тому

    It was an amazing video..

    • @Squiralnuts
      @Squiralnuts 4 роки тому

      wrong concept you providing us
      How you can say that if intersection of infinite no sets is empty how you say that the family of same sets with finite intersection also empty. For easy example let A1={2,3,4} A2={3,4,5} and A3={5,6} then intersection of A1, A2, A3 is empty, but intersection of A1, A2 ={3,4} and A2, A3={5}.
      You are wrong pls read and then teach us

    • @Squiralnuts
      @Squiralnuts 4 роки тому

      he was wrong F.I.P. fails how u can say X compact

    • @Squiralnuts
      @Squiralnuts 4 роки тому

      watch npTEL topology videos

  • @manpreetsingh2525
    @manpreetsingh2525 5 років тому +1

    Thanks ,, you made it really simple.. can you please also make videos about Alexander subbase lemma and Tychonoff theorem ?

  • @humafatima4444
    @humafatima4444 5 років тому +3

    If finite intersection property fails then how can you say that X is compact??

    • @Squiralnuts
      @Squiralnuts 4 роки тому

      wrong concept you providing us
      How you can say that if intersection of infinite no sets is empty how you say that the family of same sets with finite intersection also empty. For easy example let A1={2,3,4} A2={3,4,5} and A3={5,6} then intersection of A1, A2, A3 is empty, but intersection of A1, A2 ={3,4} and A2, A3={5}.
      You are wrong pls read and then teach us

    • @Squiralnuts
      @Squiralnuts 4 роки тому

      he was wrong F.I.P. fails how u can say X compact

    • @Squiralnuts
      @Squiralnuts 4 роки тому

      watch npTEL topology videos

  • @douglasmangini8744
    @douglasmangini8744 3 роки тому

    Great!

  • @Shahn-123
    @Shahn-123 4 роки тому

    What is website of professor Amin anyone Know please let me know

  • @mathandadventures
    @mathandadventures 6 років тому

    thanks

    • @Squiralnuts
      @Squiralnuts 4 роки тому

      wrong concept you providing us
      How you can say that if intersection of infinite no sets is empty how you say that the family of same sets with finite intersection also empty. For easy example let A1={2,3,4} A2={3,4,5} and A3={5,6} then intersection of A1, A2, A3 is empty, but intersection of A1, A2 ={3,4} and A2, A3={5}.
      You are wrong pls read and then teach us

    • @blenderstuff7861
      @blenderstuff7861 4 роки тому

      @Infinity Chess , shut up noob. Watch whole video carefully and then try to understand. Sometimes we judges someone incorrectly due to our less understanding of things. Don't judge him, he taught that correctly.

  • @Squiralnuts
    @Squiralnuts 4 роки тому +1

    wrong concept you providing us
    How you can say that if intersection of infinite no sets is empty how you say that the family of same sets with finite intersection also empty. For easy example let A1={2,3,4} A2={3,4,5} and A3={5,6} then intersection of A1, A2, A3 is empty, but intersection of A1, A2 ={3,4} and A2, A3={5}.
    You are wrong pls read and then teach us

    • @mahajan2009
      @mahajan2009 4 роки тому

      Squiral nuts the intersection of A3 and A1 is empty so the collection {A1, A2, and A3} don’t have the finite intersection property.

    • @Squiralnuts
      @Squiralnuts 4 роки тому

      @@mahajan2009 i am not saying that i am saying that intersection makes smaller set

    • @blenderstuff7861
      @blenderstuff7861 4 роки тому +1

      @Infinity Chess , shut up noob. Watch whole video carefully and then try to understand. Sometimes we judges someone incorrectly due to our less understanding of things. Don't judge him, he taught that correctly.