3 new alpha1 theorems (#1781)

Author: felixpernegger

theorems/T000895.md

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+---
+uid: T000895
+if:
+  P000174: true
+then:
+  P000210: true
+---
+
+To prove the result it is enough to show every countable subspace of $X$ is {P210}.
+Note that each subspace of $X$ is also {P174}.
+So wlog we may assume $X$ is {P57}, and hence {P28}
+[(Explore)](https://topology.pi-base.org/spaces?q=Countable%2BWell-based%2B%7EFirst+countable).
+And {T748}.

theorems/T000896.md

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+---
+uid: T000896
+if:
+  P000147: true
+then:
+  P000210: true
+---
+
+To prove the result it is enough to show every countable subspace of $X$ is {P210}.
+Note that each subspace of $X$ is also {P147}.
+So wlog we may assume $X$ is {P57}, and hence {P28}
+[(Explore)](https://topology.pi-base.org/spaces?q=Countable%2BP-space%2B%7EFirst+countable).
+And {T748}.

theorems/T000897.md

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+---
+uid: T000897
+if:
+  P000187: true
+then:
+  P000210: true
+---
+
+To prove the result it is enough to show every countable subspace of $X$ is {P210}.
+Note that each subspace of $X$ is also {P187}.
+So wlog we may assume $X$ is {P57}, and hence {P28}
+[(Explore)](https://topology.pi-base.org/spaces?q=Countable%2BW-space%2B%7EFirst+countable).
+And {T748}.