Oct 6, 2016 · 5 A topology has nothing to do with the set or the elements. Any set whether it is the set {1,2,3} {1, 2, 3} which is finite, or the set of real functions which is a higher uncountability …

Any discrete subset S of Euclidean space must be countable, since the isolation of each of its points together with the fact that rationals are dense in the reals means that the points of S …

Mar 8, 2014 · A discrete set defined hereby is essentially a formalisation of the general notion of discreteness we have used so soften. The set $\ {1, 2, 3, ..\}$ is discrete in the sense that …

Are finite sets countable by definition? I was first wondering about whether a discrete set was countable by definition, but this page states that a discrete set has to be either finite or countabl...

Feb 3, 2016 · For example. The Rational numbers aren't discrete because every interval around a rational will contain and infinite number of other rationals. The reals aren't discrete either. The …

Aug 21, 2020 · A discrete set in a metric space or other topological space, such as the line or the plane or $3$ -dimensional Euclidean space, is a space in which every points is (topologically) …

A discrete set according to Arthur's definition is automatically closed (as a point in the closure but not in the set would violate discreteness). So most likely, if you are supposed to show that the …

May 31, 2015 · 8 Abramodj: I just want to point out that closed discrete subset of a compact space is finite is consequence of a more general fact that a discrete space is compact iff it is finite. …

May 24, 2015 · I think that the correct statement is that a proper function maps closed discrete sets to closed discrete subsets. In this case D is not closed and its closure is not discrete.

Sep 3, 2017 · example of a discrete set which is closed Ask Question Asked 8 years, 3 months ago Modified 8 years, 3 months ago