Question

Let X be any set, A C X. Furthermore set T, := {0 € X| A CO}u{@} and Tz:= {0 XANO=Ø}_{x} 17,t, are called the A-inclusion, A-

(i) Show that 71,72 are topologies on X. (ii) If A =Ø, then t, = ? and T2 = ? (iii) If A = X, then T, = ? and T2 = ? (iv) Is

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Xét ( CK ) 2=1 ZEN ZEN Kul) Ciren, x angret, AEX, T2= {05X 1 Aco} N 463 Too Yoox) Ano=0} U {X} (i) I, is a topology anxi- det(11) If A=X, then I = docx 1 x Cozu{0} = & XZ 4303 = 40, x? and Tacz osxlxno=0302x? = 46303 X3 = § 6,}. (1) let x=21,2,37. A=

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