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efk
efk
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In Locally Presentable and Accessible Categories, page 12 (10),

A topological space is finitely presentable in $\mathbf{Top}$, the category of topological spaces and continuous functions, iff it is finite and discrete.

But the explanation after this sentence makes little sense to me. In particular, I want a rigorous proof that every finitely presentable object in $\mathbf{Top}$ is finite and discrete.

In Locally Presentable and Accessible Categories, page 12 (10),

A topological space is finitely presentable in $\mathbf{Top}$, the category of topological spaces and continuous functions, iff it is finite and discrete.

But the explanation after this sentence makes little sense to me. In particular, I want a rigorous proof that every finitely presentable object in $\mathbf{Top}$ is discrete.

In Locally Presentable and Accessible Categories, page 12 (10),

A topological space is finitely presentable in $\mathbf{Top}$, the category of topological spaces and continuous functions, iff it is finite and discrete.

But the explanation after this sentence makes little sense to me. In particular, I want a rigorous proof that every finitely presentable object in $\mathbf{Top}$ is finite and discrete.

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Source Link
efk
efk
  • 193
  • 6

In Locally Presentable and Accessible Categories, page 12 (10),

A topological space is finitely presentable in $\mathbf{Top}$, the category of topological spaces and continuous functions, iff it is finite and discrete.

But the explanation after this sentence makes little sense to me. In particular, I want a rigorous proof that every finitely presentable object in $\mathbf{Top}$ is finite and discrete.

In Locally Presentable and Accessible Categories, page 12 (10),

A topological space is finitely presentable in $\mathbf{Top}$, the category of topological spaces and continuous functions, iff it is finite and discrete.

But the explanation after this sentence makes little sense to me. In particular, I want a rigorous proof that every finitely presentable object in $\mathbf{Top}$ is finite and discrete.

In Locally Presentable and Accessible Categories, page 12 (10),

A topological space is finitely presentable in $\mathbf{Top}$, the category of topological spaces and continuous functions, iff it is finite and discrete.

But the explanation after this sentence makes little sense to me. In particular, I want a rigorous proof that every finitely presentable object in $\mathbf{Top}$ is discrete.

Source Link
efk
efk
  • 193
  • 6

Why finitely presentable objects in Top need to be discrete?

In Locally Presentable and Accessible Categories, page 12 (10),

A topological space is finitely presentable in $\mathbf{Top}$, the category of topological spaces and continuous functions, iff it is finite and discrete.

But the explanation after this sentence makes little sense to me. In particular, I want a rigorous proof that every finitely presentable object in $\mathbf{Top}$ is finite and discrete.