Let X = {a, b, c, d, e} and t = {X, Ø, {a} , {c, d} , {a, c, d} , {b, c, d, e}} be the topology on X and a subset A = {a, d, e} of X. Show that the relativization of t to A is TA = {A,Ø, {a} , {d},{a,d}, {d, e}}. %3D

Q: Let X={a,b,c,d}, then one of the following is a base for some topology on X: O a. {{a,b},{a,c},{a}}…

A: Base for a Topology If X is a set, then a base for a topology on X is a collection B of subsets of X…

Q: Let X = {a, b, c, d, e, f, g} and B = {{a,c, e, f}, {b, c, d, f,g}, {c}, {f}}. Show that B is a base…

A:

Q: Let X: = {a, b, c}. Y: = {1,2,3,4}. Let f:X → Y, f:= {(a, 3), (b, 3), (c, 4)}. If Ty = {Ø, X, {a,…

A: Let x:=a,b,c   y:=1,2,3,4   Let f:x→yf:=a,3,b,3,c,4  if Tx=ϕ,x,a,b,aTy:=ϕ,y,1,33,431,3,4   then f…

Q: Let U = {t,u,v,w,x,y,z), A = {u,w}, D = {x,y), C = {u,v,w), B = {u,v,w,x,z). Tell whether the…

A: Given: Let U={t,u,v,w,x,y,z}, A={u,w}, D={x,y}, C={u,v,w}, B={u,v,w,x,z}. U is the universal set.

Q: Show that there is no topology on X={a,b,c,d,e} based on the family B={{a,b},{a,b,d},{b,d,e}}

A:

Q: 4) LetXbe any set with the discrete topology. Let Y be any subset of X. Prove that ô( Y ) =Ø.

A:

Q: Let ā = ( – 5, — 4, 5) and - 4, 5) Find the projection proja b 6 and 7 = (3, 1, 0). =< of b onto a.…

A:

Q: Let à = ā ( – 5, — 4, 5) and b Find the projection of b onto a. proja b = (3, 1, 0). V

A:

Q: shows that there is no topology in X based on the family B = {{a, b}. {a, b, d}, {b, d, c}}

A:

Q: Draw a sketch of the following subsets of R². [1,2] × [1,3]

A:

Q: Prove that if U and V are neighborhoods of x e R", then so are Un V and U U V.

A: A set A is said to be neighborhood of a point x∈ℝn , if there exist a positive real number r&gt;0,…

Q: Proposition 4.4.6. A subset A of a metric space S is closed if and only if A' C A. When we…

A:

Q: Let Si = { x ∈ R ∣ x > i } , i=0,1,2,... Are the sets S1, S2, S3 . . .  are mutually disjoint?

A: If two sets A and B are mutually disjoint, then A∩B=ϕ . Define the sets S1 , S2 , S3 as follows.…