2/ Give an example of a space where the discrete topology is the same as the finite complement topology.
3/ Make and prove a conjecture indicating for what class of sets the discrete and finite complement topologies Scoincide.
4/ Define a topology on R by listing open sets within it that contains the open sets (0,1)and(1,3)and that contain and that contains as few open sets a few sets as possible.
let X be a set and assume p∈X. Show that the collection τ consisting of X and all subsets of X that exclude p, is topology on X. This topology is called the excluded point topology on X and we denote it by EPXp
Let τ consist of ∅,R and all intervals(-∞,p) for p∈R. Prove that τ is a topology on R.
This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.