Question

-5 JO1 Sewn 2.1 (2.1. Determine Int(A) and Cl(A) in each case. (a) A = (0, 1] in the lower limit topology on R. (b) A = {a} in X = {a,b,c} with topology {X, Ø, {a}, {a, b}}. A = {a,c} in X = {a,b,c} with topology {X, Ø, {a}, {a, b}}. A = {b} in X = {a,b,c} with topology {X, Ø, {a}, {a,b}}. A = (-1, 1) U {2} in the standard topology on R. (f) A = (-1, 1) U {2} in the lower limit topology on R. A = {(x,0) ER| XER} in R2 with the standard topology. (h) A = {(0, x) € RP | X < R} in R2 with the topology generated by the basis in Exercise 1.19. (i) A = {(x,0) € RR} in R2 with the topology generated by the basis in Exercise 1.19.

please explain in detail, for each part, especially for parts (g)-(i).

*Here is the information about the basis for (h) and (i), it is the basis that generates the vertical interval topology on R^2:

Answer 1

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