Differential Geometry | Topology Answers

Show that the set S={{x}│x∈X} being a sub base generates a discrete topology on any set X

Suppose that A⊂B⊂X and A is dense in closure of B and B is dense in X.
Then A is also dense in X.

Prove that intersection of two dense subsets is again dense subset

Let X={a,b,c,d} with the topology T={ ϕ,{a},{a,b},{a,b,c,d}}. Find all the homeomorphism f:X->X and jastify that your list is exhaustive.?

what is poincare conjecture and this prove

Dear Expert how will we show that a coffee cup is homeomorphic to doughnut .f any approach please explain.

Expert sir if a topology is neither discrete nor indiscrete is called what?by which name we represent a topology that is neither discrete nor indiscrete?

find the limit points and closure of z and Q in R.best regards

Dear Expert sir what is a a topological property

Need help with following Q:

X is the ray {0,infinity) and the topological structure consists of {}, X, and all rays (b, infinity) with b>=0. Please prove that every continuous bijection of this space X onto itslef is a homeomorphism.

Thank you very much.