WebEvery point in S is its own open set. The integers are discrete in the reals, but the rationals are not. In the indiscrete topology, only the empty set and the entire set are open and … WebFeb 17, 2024 · If every infinite subset of X is declared open, then this topology is the discrete topology, not the indiscrete one. To see this, take an arbitrary countably …

The Discrete Topology - Colorado State University

Web1. The Discrete Topology Let Y = {0,1} have the discrete topology. Show that for any topological space X the following are equivalent. (a) X has the discrete topology. (b) Any function f : X → Y is continuous. (c) Any function g : X → Z, where Z is some topological space, is continuous. Proof. (a ⇒ c) Suppose X has the discrete topology ... Web1.The collection T=P(X) is defined to be the discrete topology. 2. The collection T= ff;Xgis defined to be the indiscrete topology. It is also sometimes referred to as the trivial topology. Lemma 1.2.1 For any set X, the discrete topology and indiscrete topology are well-defined topolo-gies on X. Proof. First we consider the discrete topology. cmich international

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WebIn topology, a topological spacewith the trivial topologyis one where the only open setsare the empty setand the entire space. Such spaces are commonly called indiscrete, anti-discrete, concreteor codiscrete. Intuitively, this has the consequence that all points of the space are "lumped together" and cannot be distinguishedby topological means. WebDiscrete and Indiscrete topology types of topologies Math Brain 2.72K subscribers Subscribe 165 Share Save 6.8K views 2 years ago different type of topologies, discrete … cafe geyer hamburg