Completing Poset with Alexandrov topology (S152)

spaces/S000152/properties/P000204.md

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+---
+space: S000152
+property: P000204
+value: false
+---
+
+Given $x\in X$, there is a largest point $y\in X\setminus\{x\}$.
+Every nonempty open set of the subspace $X\setminus\{x\}$ contains $y$,
+and therefore $X\setminus\{x\}$ is {P39} and thus {P36}
+[(Explore)](https://topology.pi-base.org/spaces?q=Hyperconnected+%2B+%7EConnected).