John
Reputation
1,360
Next privilege 2,000 Rep.
 Aug 24 answered What is the smallest cardinality of a Kuratowski 14-set? Aug 23 comment What is the smallest cardinality of a Kuratowski 14-set? Perhaps you are thinking of exercise 21 page 102 in "Topology" 2nd ed. by Munkres. In part a) we are asked to prove Kuratowski's original result. If I am not mistaken an answer for b) is given by the set $\{0\}\cup(1,2)\cup(2,3)\cup(Q\cap(3, 4))$. The question I posted here was motivated precisely by this part b). I would like to find the smallest possible set that generates 14 differents sets. Aug 23 asked What is the smallest cardinality of a Kuratowski 14-set? Jun 9 awarded Supporter Jun 9 answered $X$ and $Y$ are homotopy equivalent $\Leftrightarrow$ $\exists Z:$ $X,Y$ are strong deformation retracts of $Z$ May 7 awarded Scholar May 7 accepted A contractible mapping cone? May 6 comment Showing that metric induces single unique topology on a finite set Your argument shows that any metric defined on a finite set will induce the discrete topology on that set. Therefore, the discrete topology is the only one that can be induced by a metric on a finite set. May 6 revised Topological Properties of a 3-Torus improve the wording of a statement May 6 revised What are some examples of a mathematical result being counterintuitive? Example added to improve clarity May 6 revised Topological Properties of a 3-Torus Improve clarity May 6 revised Topological Properties of a 3-Torus Expanded answer May 4 answered What are some examples of a mathematical result being counterintuitive? May 4 awarded Teacher May 4 answered Topological Properties of a 3-Torus May 3 comment A contractible mapping cone? The motivation for this exercise is the following result: If two maps are homotopic, their mapping cylinders (and hence their mapping cones) are homotopy equivalent. Therefore, one can show that the dunce cap is contractible because it is easily seen to be homeomorphic to the mapping cone of $f$. May 1 answered A contractible mapping cone? May 1 revised A contractible mapping cone? Clearing up the style, as I was able to provide an answer Apr 30 comment A contractible mapping cone? @Justin: Got it, thanks! I guess I need to take a complex analysis course. How did you construct $H$? Apr 30 awarded Editor