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Thread: rational sequence topology

  1. #1
    Nov 2011

    rational sequence topology

    let x be the set of real numbers and for each irrational x we choose a sequence {x$\displaystyle i$} of rationals converging to it in the euclidean topology .the rational sequence topology is the defined by declaring each rational open, and selecting the sets U$\displaystyle n$(x)={x$\displaystyle i$}(n from 0 to infinity) U {x} as a basis for the irrational point x.

    can anyone tell me the following properties regarding the above topological space?

    - basis
    -sub basis
    -interior and closure
    -Both Open and Closed Sets
    -Hausdorff Space and Metrizable Topology
    -Relative Topology
    -Finer and Coarser Topology
    Last edited by rachit6542; Nov 7th 2011 at 12:28 AM.
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  2. #2
    Senior Member Tinyboss's Avatar
    Jul 2008

    Re: rational sequence topology

    Eleven questions in your first ever post? That's got to be some kind of record!

    Seriously, though: if you want to get a helpful reply, you should tell us what you've attempted already and where you're stuck, and possibly focus on one question at a time. (DON'T break it up into 11 separate topics and post them all at once!)

    And if you haven't attempted anything yet because you don't know where to start, then re-read the chapter, asking yourself as you read each theorem and definition whether you can apply it to your current problem.
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