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.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Is there any space with such properties? If there is no such space, I would be very grateful if you could tell me proof of this fact.

share|cite|improve this question
Er...any singleton? – DonAntonio Mar 25 '13 at 15:02
up vote 2 down vote accepted

There is a construction which associates a topological space to any poset. Under this construction finite posets gives rise to finite topological spaces. It is known that the space is contractible if the poset has maximum (or minimum). This construction gives you a lot of examples. For instance the example of Arthur Fischer correspond with the poset with 2 (comparable) points.

EDIT: It is "easy" to construct examples of simply-connected non-contractible spaces. An easy one is the space associated to the poset $P=\{(a,b): a=0,1; b=0,1,2\}$ where $(a,b)<(a',b')$ if $b<b'$ (this is a model of $S^2$).

share|cite|improve this answer

The Sierpiński space is contractible, hence simply connected.

share|cite|improve this answer

Your Answer


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.