The subspace A = [0,12)∪(12,1] of I is locally connected as its components are also connected but it is not connected as we can choose open sets B = (-1,12) and C =(12,2) such that A⊂B∪C and A ∩B≠∅ and A ∩C≠∅ and A ∩B∩C=∅ \text{The subspace A = [0,$\frac{1}{2})\cup(\frac{1}{2},1]$ of I is locally connected as its components are also }\\\text{connected but it is not connected as we can choose open sets B = (-1,$\frac{1}{2})$ and }\\\text{C =($ \frac{1}{2}$,2) such that A$\subset B \cup C$ and A $\cap B \neq \emptyset$ and A $\cap C \neq \emptyset$ and A $\cap B \cap C = \emptyset$ }The subspace A = [0,21)∪(21,1] of I is locally connected as its components are also connected but it is not connected as we can choose open sets B = (-1,21) and C =(21,2) such that A⊂B∪C and A ∩B=∅ and A ∩C=∅ and A ∩B∩C=∅
Need a fast expert's response?
and get a quick answer at the best price
for any assignment or question with DETAILED EXPLANATIONS!
Comments
Leave a comment