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Given a set $X$, is there a topology $\tau$ such that the identity $\text{id}_X$ on $X$ is the only continuous injective self-map?

(This is Joel David Hamkins's recent questionJoel David Hamkins's recent question in the category $\mathbf{Top}^\text{op}$.)

Given a set $X$, is there a topology $\tau$ such that the identity $\text{id}_X$ on $X$ is the only continuous injective self-map?

(This is Joel David Hamkins's recent question in the category $\mathbf{Top}^\text{op}$.)

Given a set $X$, is there a topology $\tau$ such that the identity $\text{id}_X$ on $X$ is the only continuous injective self-map?

(This is Joel David Hamkins's recent question in the category $\mathbf{Top}^\text{op}$.)

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Dominic van der Zypen
Dominic van der Zypen
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Injectively rigid spaces

Given a set $X$, is there a topology $\tau$ such that the identity $\text{id}_X$ on $X$ is the only continuous injective self-map?

(This is Joel David Hamkins's recent question in the category $\mathbf{Top}^\text{op}$.)