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B) closed but not open Chopen D) closed and continuous. 7) The function f : (R,Tsorg) → (R.T.); f(x,y) = [x] = the largest integer s xis A)open and continuous B)continuous Chopen D)homeomorphism 8) The sequence f(n) = (1 + (11n)]" is an increasing sequence of rationals (Math.102). In topology, ACC ((-1)"f(n), (RTU)= A){2.71} B) {3} C){2} D) {e,-e} 9) Let f:(RTL...) (RT) be a continuous function, where {(x,x):X ER} is a closed set in the product space of (R,T) with itself. Then A) f(x)=x for every x in R B) f(x)= x for all x in R C) f(x) =x for some x in R D)None of the above. 10) If (X,T) is second countable and T1.5-space. Then (X,T) is A)Hausdorff B)locally connected C) pathwise connected DN.A. 11) If X is a countable set and (X,T) is first countable, then (X,T) is A) pathwise connected B) zero-dimensional C) second countable space D) N.A. 12) In (R,TL.r.), if A={XER:#²24}, then Int(A)= A) (2, c). B) (-0,2) C) (-2,-2) D) (-2,2] 13) The countable collection 2 = {[a,b:a,beQ) is a base for the following topology on X=R: A) Tsorg B) TU C) Toc D) N.A. 14) If (X,T) is a T -space and XxX\ = 144. Then 7 = A) 2 B) 84 C) 2144 D) N.A. 15) A retract of a connected T4-space must be: A) connected and TA B) Locally connected C) pathwise connected D) N.A. 16) The followings have the fixed point property: A) (R, Tinc, n) and ([e, x), Tu) B) (R,Tinc, 12.43) C) (R,Tsorg) D) ([1,6], Tdis)