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- Homework Statement
- Verify that the “weakest” (coarsest) possible topology on a set ##X## is given by the trivial topology, where ∅ and ##X## represent the only open sets available, whereas the “strongest” (finest) topology is the discrete topology, where every subset is open.

- Relevant Equations
- 1. ∅ ∈ {τ}, ##X## ∈ {τ};

2. the union (of an arbitrary number) of elements from {τ} is again in {τ};

3. the intersection of a finite number of elements from {τ} is again in {τ}.

I do not understand what is to verify here. The problem already defined what it means to be a trivial and discrete topology but it did not state what it means to be "weak" and "strong". I assume the problem wants me to connect "weak" with trivial topology and "strong" with discrete topology, but somehow the problem is not very clear to me or I just do not know how to connect them. Please guide me but do not give me the solution.