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 | | From: | Valeriu Anisiu | | Subject: | Re: Homeogeneous Spaces | | Date: | Mon, 24 Jan 2005 00:09:40 +0000 (UTC) |
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 | On 23 Jan 2005, Valeriu Anisiu wrote:
>On 23 Jan 2005, William Elliot wrote:
>>Topological space S is homogeneous when for all x,y in S,
>> some auto-homeomorphism h:S -> S with h(x) = y.
>>
>>Is a connected subspace of homogeneous space homogeneous?
>> No. [0,1] and [0,1) subset R are counterexamples.
>>
>>Is an open subspace of homogeneous space homogeneous?
>>Is an open connected subspace of a homogeneous space homogeneous?
>>
>>Counter examples, of course, are welcome.
>>
>>----
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>No.
>S=[0,1] with the natural topology is homogeneous,
>[0,1) is open and connected _in S_ but it is not homogeneous.
>
>V. Anisiu
Sorry, S is not of course homogenous.
V.
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