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P234: CGS terminology
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properties/P000234.md

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@@ -4,6 +4,8 @@ name: Has open connected components
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refs:
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- mathse: 3002235
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name: Answer to "Definition of locally pathwise connected"
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- zb: "0451.54017"
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name: Topologies determined by paths (S. Franklin, B. Smith-Thomas)
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---
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Every connected component of $X$ is open.
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The equivalence between the various conditions can be shown by arguments similar to those used in the definition of {P42}, in particular {{mathse:3002235}}.
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This property is normally used without a separate name. But see {{zb:0451.54017}}
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(accessible [here](https://topology.nipissingu.ca/tp/reprints/v04/tp04204.pdf)),
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where it is called "CGS" (connectedly generated space).
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Compare with {P41} and {P233}.
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