Why the union of countable sets is countable? Why cannot we use the powerset as the sample space? Why is the empty set called a proper set? How to prove whether a set is a closed set? How to prove that the closure of a set is closed?
A locally compact space X is said to be countable at infinity if it is the union of countably many compact subsets. Compact spaces are countable at infinity. The space ℝn is countable at infinity, since it is locally compact and may be written as the union of the Bc (0; m) such...
How to prove every finite set is countable? How do you prove every finite set is countable? Show by example that arbitrary intersections of open sets may not be open and that arbitrary unions of closed sets may not be closed. How to prove that a set is dense? What is an open set in...
How to prove something is closed under addition? How to prove something is not closed under addition? How to tell if a set is transitive? Prove the following using the element method for prove that a set equals the empty set : For all sets A and B Prove or disprove the following: If ...
we determine the behavior of soft generalized ω -closed sets relative to soft unions, softintersections, soft subspaces, and generated soft topologies. Furthermore, we investigate soft imagesand soft inverse images of soft generalized closed sets and soft generalized ω -closed sets undersoft continu...