Conponent wrong use of name?

  • Thread starter jessicaw
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  • #1
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conponent(maximal connected set) must be closed, connected, open, disjoint. This is a fact.
But why people still say somthing redundant like "closed connected component", "open disjoint component", "connected disjoint component"? Is it really redundant or my concept not clear?
 

Answers and Replies

  • #2
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Firstly, a component is not necessairily open. Take, for example, the components in Q, these are the singletons and are not open.

Why people say closed connected component? Depends of the situation. But my guess is that the want to emphasize that they're closed. Can you give an example on when they use it?
 
  • #3
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but why people always say"connected component" but not just "component"? Nearly every book or website use the former term.
 
  • #4
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There are other forms of components. We also have the quasicomponents (these are the intersection of all clopen sets containing a point). I guess people say "connected component" because they don't want confusion with other kinds of components...
 

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