A computer is infected with the Sasser virus.
A computer is infected with the Sasser virus. Assume that it infects 20 other computers within 5 minutes; and that these PCs and servers each infect 20 more machines within another five minutes, etc. How long until 100 million computers are infected?
sierpinski space is contractible
Let X be Sierpinski space: X={x,y} with topology {X,empty set, {x}} . prove that X is contractible.
Give proofs or counter-example for the following statements: i)If X and Y are path connected subsets of Z and X/Y ( X intersection Y) is non empty then X/Y is path connected. ii) If X and Y are path connected subsets of Z the X/Y(union) is path-connected. iii)If X and Y are path connected subsets of Z and X/Y ( X in ...continues
Topological Groups : Quotient and Open Maps
Let be p:G to G/N a quotient map.Is it open? Let be f:G to H an open map. Is it quotient map? Here G and H are topological groups, and N is an subgroup.
Continuous Maps, Homomorphisms and Cyclic Groups
Let f: S^n --> S^n be a continuous map. Consider the induced homomorphism f*: H~_n (S^n) --> H~_n (S^n), where H~_n is a reduced homology group. Then from the fact that H~_n (S^n) is an infinite cyclic group, it follows that there is a unique integer d such that f*(u) = du for any u in H~_n (S^n). How exactly does "ther ...continues
Covering space of S^1 and Homomorphisms
Let p: (0,10) --> S^1, p(t) = (cos t, sin t). Show that p is a local homomorphism, but ((0,10), p) is NOT a covering space of S^1
Tychonoff and Hausdorff Spaces
Let X and Y connected, locally path connected and Hausdorff. let X be compact. Let f: X ---> Y be a local homeomorphism. Prove that f is a surjective covering with finite fibers. Prove: a) Any subspace of a weak Hausdorff space is weak Hausdorff. b)Any open subset U of a compactly generated space X is compactly generated ...continues
Contractible Spaces : Homotopy Type
How can I show that the two contractible spaces have same homotopy type? keywords: homotopic
Homotopy Types and Equivalence Relations
Prove that "having the same homotopy type" is an equivalence relation on the set of topological spaces. keywords: homotopic
Free Groups : Show that G1*G2 is not abelian and must contain an element of infinite order.
Show that G1*G2 is not abelian and must contain an element of infinite order.
