## Topology## MotivationMany proofs are based on the same key ideas. It is good to isolate the key ideas in as general form as possible and then derive results there. ## DefinitionA - 1) For any collection of elements of τ, the union of them is in τ.
- 2) For any finite collection of elements of τ is in τ.
- 3) The entire set X and the empty set are members of τ.
τ is called ## Trivial CasesAny set X can be made into a topological space by taking either (discrete topology) or by taking τ={X,0} (the indiscrete topology). ## Interesting CasesLet X=R (the set of real numbers) and let τ=all subsets of R which can be expressed as unions of open intervals (a,b). Author: Danny (remove the ".nospam" to send) Last modification on: Sat, 04 May 2024 . |