IIT JAM
Shweta Singh Asked a Question
January 11, 2020 1:20 pmpts 15 pts
  • IIT JAM
  • Mathematics (MA)

Let S be a non empty set and F be a field, for any S ES define W=lf€F{S, F]:f(s,=0} W=lf€F|S,F}:fls)=0 for all but a finite number of elements of S}, where F(S,

Let S be a non empty set and F be a field, for any S ES define W=lf€F{S, F]:f(s,=0} W=lf€F|S,F}:fls)=0 for all but a finite number of elements of S}, where F(S,F) denotes the set of all functions from S to F. then only W, is a subspace of F(S,F) only W2 is a subspace of F(S,F) Both W, and W, is subspace of F(S,F) Neither W, nor W is subspace of F(S,F)
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  • Eduncle Best Answer

    Dear Shweta,

    Greetings!!

    Refer the attached image for solution.

    Thank you for asking your query.

    • maths181.JPG
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  • Nikihi
    fhddghnb
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  • P Choursiya
    if you have any query, reply me. this question is good. this question involve countability. to make W be subspaces it is needed that it is closed. in general we show that a+b for ...
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