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01.14.2008 at 03:09PM PST, ID: 23082487
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component of a connected topological space

Asked by rabroersma in Math & Science Questions, Miscellaneous

Here are some definitions:
A topological space S is connected if emptyset and S are the only subsets of S that are both open and closed.  A subset of S is connected if it is connected in the relative topology,  A component, B, of S, is a nonempty connected subset of S such that the only connected subset of S constaining B is B itself.  

The question is:  is B open and closed in both the relative topology of B, and also in S?Start Free Trial
[+][-]01.14.2008 at 03:36PM PST, ID: 20658442

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[+][-]01.14.2008 at 07:04PM PST, ID: 20659716

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[+][-]01.14.2008 at 08:53PM PST, ID: 20660231

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[+][-]01.14.2008 at 08:54PM PST, ID: 20660237

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[+][-]01.15.2008 at 04:33AM PST, ID: 20661906

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Zones: Math & Science Questions, Miscellaneous
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Solution Provided By: BigRat
Participating Experts: 3
Solution Grade: C
 
 
 
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20080716-EE-VQP-32 / EE_QW_2_20070628