Find an example of a topological space with a topology different from the indiscrete topology in which every subset is connected Find an example of a topological space with a topology different from the indiscrete topology in which every subset is connected. I can only think of a space with one single point, but then every topology will be the indiscrete topology.

If $A = \\{ a,b \\}$ with topology $\tau = \\{ \varnothing, \\{a\\}, A \\}$, then it is not the indiscrete topology.
Isn't this one connected?

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**Edit:**
This is the Sierpiński space.
And it is indeed connected.