Re: subcontinua
From: Ali Taghavi (taghavi_at_ipm.ir)
Date: 01/25/05
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Date: Tue, 25 Jan 2005 15:00:06 +0000 (UTC)
This reminds me the following theorem and question(the theorem can be
found in the book "Topology" by Hocking and Young
Th:A metric space which is continum can not be decomposed to disjoint
union of countable number of closed subsets
Question:Do you have a counterexample of decomposition of a connected
metric space(Not necessarily compact)to countable number of closed
subsets?
Ali Taghavi
On 21 Jan 2005 07:45:03 -0500, K. P. Hart wrote:
>
>Michael Hamm wrote:
>
>>Anyone have any idea what a subcontinuum is? I cam across the term
in a
>>1938 paper: "compact, proper subcontinua" of a surface or of a
connected,
>>locally connected, cyclically connected, compact space.
>>
>>
>The best I can say is this:
>a continuum is a compact connected Hausdorff space and a
>subcontinuum of a space is a subspace of the space that is a
continuum.
>KP
>
>--
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href="http://fa.its.tudelft.nl/~hart">http://fa.its.tudelft.nl/~hart>
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