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anonymous

  • one year ago

Which of the following spaces is Hausdorff?

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  1. anonymous
    • one year ago
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    @zzr0ck3r

  2. anonymous
    • one year ago
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    The discrete space

  3. anonymous
    • one year ago
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    The indiscrete space

  4. anonymous
    • one year ago
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    R with the finite complement topology

  5. anonymous
    • one year ago
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    X = [a,b] endowed with the topology \[\tau \] = (\[ϕ \],X,[a])

  6. zzr0ck3r
    • one year ago
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    ok, a space is Hausdorff if for any two elements, there is an open nbhd around each that does not intersect each other. If every set is open, what do we call this space?

  7. anonymous
    • one year ago
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    discrete topology

  8. anonymous
    • one year ago
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    @zzr0ck3r

  9. anonymous
    • one year ago
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    A set is nowhere dense if the set \[barA \] has empty

  10. anonymous
    • one year ago
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    i think interior ????????????????

  11. anonymous
    • one year ago
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    @zzr0ck3r

  12. zzr0ck3r
    • one year ago
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    Sorry, I was helping someone before you texted me and I did not think it would take this long.

  13. zzr0ck3r
    • one year ago
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    wait, are you asking another question now?

  14. anonymous
    • one year ago
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    yes

  15. anonymous
    • one year ago
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    i think the answer to the first question is the discrete space

  16. zzr0ck3r
    • one year ago
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    it is not

  17. zzr0ck3r
    • one year ago
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    why do you think that?

  18. zzr0ck3r
    • one year ago
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    dont just move on....answer me :)

  19. anonymous
    • one year ago
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    because discrete topology is one that has every set open

  20. anonymous
    • one year ago
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    so sorry if i am wrong

  21. zzr0ck3r
    • one year ago
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    oh sorry, I thought you asked for the non Hausdorff one...you are correct. But let us not move on...

  22. zzr0ck3r
    • one year ago
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    why does every set being open mean that it is Hausdorff?

  23. anonymous
    • one year ago
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    ok thank you sir . a big hug

  24. anonymous
    • one year ago
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    because there intersection will give the empty set

  25. zzr0ck3r
    • one year ago
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    what intersection?

  26. zzr0ck3r
    • one year ago
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    who is they?

  27. anonymous
    • one year ago
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    a space is Hausdorff if for any two elements, there is an open nbhd around each that does not intersect each other

  28. anonymous
    • one year ago
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    that was what you said

  29. zzr0ck3r
    • one year ago
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    but you did not show me the sets. Here is the proof, and this is what I am looking for. Suppose \(x_0, x_1\in X\). Then \(\{x_0\}\) and \(\{x_1\}\) are both open sets, and \(\{x_0\}\cap\{x_1\}=\emptyset\).

  30. anonymous
    • one year ago
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    ok. thank you sir

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