Convergent sequences in topological spaces

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  • Опубліковано 22 гру 2024

КОМЕНТАРІ • 12

  • @ciokas
    @ciokas 4 роки тому +6

    Great stuff, helped me understand convergence without the notion of distance. Thank you!

  • @monicamiranda3161
    @monicamiranda3161 2 роки тому

    I need a definition of convergence in topological spaces, but out of metric spaces. A definition that would not use distance. As the problems that I had in mathematical physics had nothing to do with distance. It was in the topological space and out of any metric space. I was in a space that admitted no distance and even though I had convergence of sequences.
    This is what I an looking for and I could put my imagination to work how it might be, but my imagination is not good nowadays.
    And yes, I need this and I think I will have a hard time trying to find. People come around with real analysis concepts and distances and I was not in this realm, if you know what I mean.

  • @monicamiranda3161
    @monicamiranda3161 2 роки тому

    that topological space X={a,b,c} where the sequence is a sequence in X and x belongs to X then -->x looks like a chaotic topological space , since x € {a,b,c}, that is , any sequence converges to any point.
    That was given me as a counter example in a class and I am looking for more meaningful sequences in topological spaces.
    I am trying hard to fill my gaps to understand moduli spaces.
    I know there are people here that did not understand configurations in moduli spaces and they are doing wrongs things here. They are using all those configurations and configurations of configurations to program robots to do some kinds of simulations for them. You cannot reach a right result , if you come from wrong premises and have lots of gaps in your math background.
    We have reached a strange reality that is not reality at all. I myself feel like the Mad Hatter stuck at tea time.
    What can I say to those people? That they don't have o'clock? Their problem is much bigger. They are causing an ontological problem in our reality. There's an Y there that nobody knows about of its existence. But Y is not the only one , there's a W, a Z, a V, etc that nobody knows about their existence.
    My job now is to tell people of beings they did not know existed on the planet . When the White Knight gave Alice a recipe of a dessert, what was he's meaning for her to do? To catch a proof of a being on her reality that she did not know it existed.
    All those beings subreptciously trying to change our reality are part of an ontological problem that we must solve bringing them all to day light. Once they are presented to humanity they will lose their power and humanity will gain power that she lost long ago.
    "who is she fairer than the moon , brighter than the sun terrible as an army arrayed to battle with banners?"

  • @satyampandey9550
    @satyampandey9550 2 роки тому +1

    Thanks teacher there is language problem for me 😞
    But I understand thanks
    Sir if we take X={1,2} and £={phi , {1},X} then (X,£) is topological space so can we say there is seqn in X:1,1,1..... Convergent to 1 has unique limit exit

    • @DrMcCrady
      @DrMcCrady  2 роки тому +2

      Yes that’s right, since every neighborhood of the limit point 1 (only have to consider {1} and X) has an element of the sequence (namely 1). The space you listed is also interesting because if you take the sequence (1,2,1,2,…) then the limit is 2, because there is only one neighborhood of 2, namely X, and this neighborhood certainly contains all points from the sequence. That demonstrates how important the topology is when you determine limits. The latter example is weird because there aren’t many neighborhoods consider in that topology.

    • @satyampandey9550
      @satyampandey9550 2 роки тому

      @@DrMcCrady yes sir thanks teacher ❤️🙏🙏

    • @monicamir
      @monicamir 2 роки тому

      A sequence where xi= 1 for all i in N is a trivial sequence that converges to 1.
      How about a chaotic topological space where any sequence converges to any point?
      It's hard to define sequences in topological spaces out of metric spaces and everybody falls in analysis in R not even in metric spaces.
      I can't buy a book here and I have to use my ìmagination .

  • @suayhossien
    @suayhossien 4 роки тому +1

    Nice