Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

This is an exercise from a topological book.

Show that the Sorgenfrey line and the Niemytzki plane are not homeomorphic.

Thanks for any help.

share|improve this question
    
Is the question really concerning Sorgenfrey line vs Niemytzki plane or should it maybe be Sorgenfrey plane vs. Niemytzki plane? –  Sam Aug 9 '12 at 13:40
    
It is really concerning Sorgenfrey line vs Niemytzki plane. It is from Engelking's book. –  Paul Aug 9 '12 at 13:50

2 Answers 2

up vote 2 down vote accepted

HINT: The Niemycki plane has a closed, discrete set of cardinality $2^\omega$. Does the Sorgenfrey line?

share|improve this answer
    
Mm it don't seems to have such set, however its square seems to have such set. –  Paul Aug 9 '12 at 13:32
    
That’s correct. To show that it does not have such a set, let $A$ be an uncountable subset of the Sorgenfrey line, and show that $A$ must have an accumulation point. –  Brian M. Scott Aug 9 '12 at 13:42

Help:

Find a topological difference between the two. To do this you will have to think about the definitions of everything involved.

After you do that, be sure to add to your question to include what work you've done, so it doesn't sound so much like a demand.

share|improve this answer
    
Thanks for your response! –  Paul Aug 9 '12 at 13:33

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.