add connectedness properties

spaces/S000199/properties/P000039.md

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+---
+space: S000199
+property: P000039
+value: true
+---
+
+Every pair of basic open sets $(\leftarrow,m)$ and $(\leftarrow,n)$
+intersects.

spaces/S000199/properties/P000040.md

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+---
+space: S000199
+property: P000040
+value: true
+---
+
+$0$ is in the closure of every non-empty set.

spaces/S000200/properties/P000039.md

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+---
+space: S000200
+property: P000039
+value: true
+---
+
+Every pair of basic open sets $[m,\rightarrow)$ and $[n,\rightarrow)$
+intersects.

spaces/S000200/properties/P000040.md

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+---
+space: S000199
+property: P000040
+value: true
+---
+
+Let $m\in M$ and $n\in N$ be members of closed sets $M,N$.
+Then every neighborhood of $m$ contains $n$, so $m$ is a
+limit point of $N$, showing $m\in M\cap N$.