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Possible Duplicate:
Two questions on Sorgenfrey line

This is an exercise from Engelking's Book.

Verify that the Sorgenfrey line can be mapped onto $D(\aleph_0)$, but cannot be mapped onto $D(2^\omega)$?

I don't how to show it. Could anybody help me? Thanks ahead.

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    I believe this is a duplicate of (half of) [this question](http://math.stackexchange.com/q/162271/8348).2012-08-09
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    Please do not delete questions when you received an answer.2012-08-09
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    @t.b. However, Arthur gives me a link for the question; and he have given an answer there.2012-08-09
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    And that's a reason to delete the thread and to ensure that Brian's time is completely wasted?2012-08-09
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    There were related discussions at meta: [Policy on users deleting their own questions?](http://meta.math.stackexchange.com/questions/4332/policy-on-users-deleting-their-own-questions) and [What should be deleted? If I realize a question is pointless?](http://meta.math.stackexchange.com/questions/1153/what-should-be-deleted-if-i-realize-a-question-is-pointless)2012-08-09
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    @t.b. I thank Brain very much; However I see many of us choose to close the question for the question lose its sense. So I choose to delete. I will keep it if you believe it need to exist here still.2012-08-09
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    @Martin Thank you for the link. I will read it.2012-08-09
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    And also this: [On deleting vs. closing duplicate questions.](http://meta.math.stackexchange.com/questions/3338/on-deleting-vs-closing-duplicate-questions). All three can be briefly summarized in a way, that it is frowned upon.2012-08-09

1 Answers 1

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HINTS:

  1. The Sorgenfrey line is the union of the sets $[n,n+1)$ for $n\in\Bbb Z$.

  2. The Sorgenfrey line is separable. A continuous map onto $D(2^\omega)$ would contradict this; how?

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    @Brain Thanks for your answer. It is very helpful for me. I'm very happy to see you here. Long time I have not seen you.2012-08-09
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    @Brain Could you help me to solve this question.http://math.stackexchange.com/questions/173859/a-question-on-a-quotient-of-alexandroffs-double-segment-space It has posted a long time. But I have not got a good answer.2012-08-09
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    @Paul: Take a look: I just posted an answer.2012-08-09
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    @Brain Thanks. I will go.2012-08-10