Consider the following topology T on the set X = {a, b, c, d, e}:

T = {{a}, {b, c, d}, {e}, {a, b, c, d, e}, ?}

1. Determine if T is a topology on X. If it is a topology, prove it. If it is not a topology, provide a counterexample. (5 marks)

2. Find the closure of the set A = {b, c} with respect to T. (5 marks)

3. Is X a compact space with respect to T? If it is compact, prove it. If it is not compact, provide an open cover of X that has no finite subcover. (10 marks)

Answer rating: 100% (QA)

The detailed answer for the above question is provided below To check if T is a topology on X we need to verify the three conditions for a collection of subsets of X to be a topology X and the empty s... View the full answer