add continuum and theorems (#628)

properties/P000188.md

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+---
+uid: P000188
+name: Continuum
+aliases:
+  - Hausdorff continuum
+refs:
+  - doi: 10.1016/B978-0-444-50355-8.X5000-4
+    name: Encyclopedia of General Topology (Hart et al)
+  - doi: 10.1201/9781315274089
+    name: "Continuum Theory: An introduction (Nadler)"
+---
+
+A {P3}, {P16}, and {P36} space, as defined in e.g.
+{{doi:10.1016/B978-0-444-50355-8.X5000-4}}.
+
+Note that many authors (e.g. {{doi:10.1201/9781315274089}}) use the
+term "continuum" to refer to spaces that are also {P53}, which is
+not assumed here.

theorems/T000480.md

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+---
+uid: T000480
+if:
+  and:
+    - P000016: true # compact
+    - P000036: true # connected
+    - P000003: true # T2
+then:
+  P000188: true # continuum
+---
+
+By definition.

theorems/T000481.md

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+---
+uid: T000481
+if:
+  P000188: true # continuum
+then:
+  P000003: true # T2
+---
+
+By definition.

theorems/T000482.md

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+---
+uid: T000482
+if:
+  P000188: true # continuum
+then:
+  P000016: true # compact
+---
+
+By definition.

theorems/T000483.md

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+---
+uid: T000483
+if:
+  P000188: true # continuum
+then:
+  P000036: true # connected
+---
+
+By definition.