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Vijay posted an Question

April 11, 2021 • 12:56 pm

30 points

IIT JAM
Mathematics (MA)

Please send the solution to the problem given in the attachment.

please send solution to the problem given in the attachment

1 Answer(s)

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A
Alka gupta

if A is any set then generally A' denotes derived set of A( set of all the limit points of A) so in your qus they written correct
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see
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now what you say?
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yes...they want to say nbd of a and b not subset of (a,b] and [a,b)...it means a,b are not interior points
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Deepak singh 1 Best Answer

Here , D' denotes set of limit points . So if D=[0,1) then D'= [0,1] is correct ..
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if here D' is denoting set of interior points , then D'=(0,1)
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acc. to the definition, 1+€ does not belong to the set D, that is why I raised the question.
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first of all tell , what D' is denoting here.? we usually denotes it as set of limit points of set D.
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yes , you are correct , if we talk about interior points . epsilon neighborhood of 1 ( I.e (1-€,1+€) ) will doesn't contained in D =[0,1) So set of interior points of D = (0,1)
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D' is derived set i.e. set of all limit points.
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then D'= [0,1] is correct .
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see
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its definition of neighborhood not definition of limit points..
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ok
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