Question: Could someone please check my work? Given that F= E ( t , 1)inEIN, no 13. why is This family of Sets not an open

Could someone please check my work?

Given that F= E ( t , 1)inEIN, no 13. why is This family of Sets not an open cover of [o, 1]. Because it doesn't contain its cluster points, O'andl. The gap between ~ and O becomes infinitesimally Small, but is never covered by The family [0, 17 4 ( 2, 1) = ( 5 , 1) = ( 4, 1) c ... ( 2, 1 ) There is also a gap in The open cover at 1. Hence [0, 1 ] $ UF since it is not The case That every point in [0 , 1) is contained in The union of all open sets in F

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