2025年1月31日 · A discrete space is simply a topological space equipped with the discrete topology. A discrete space is always a metric space, namely the metric space with the same …

In the narrow sense, a space with the discrete topology. In the broad sense, sometimes termed Alexandrov-discrete, a topological space in which intersections of arbitrary families of open …

2025年1月31日 · A topology is given by a collection of subsets of a topological space X. The smallest topology has two open sets, the empty set emptyset and X. The largest topology …

2023年11月3日 · To begin with, what are your definition of "discrete space" (there are many equivalent definitions), and of the natural topology of your subset " 1/N 1 / N " of R R? Or from …

2018年2月10日 · The discrete topology on a set X is the topology given by the power set of X. That is, every subset of X is open in the discrete topology. A space equipped with the discrete …

2016年10月6日 · A discrete space is one in which the single point sets are defined to be open. If, for $S=\{1,2,3 \}$ we declare: $\varnothing , \{1 \}, \{2 \},\{3 \},\{1,2 \},\{1,3 \},\{2,3 \},\{1,2,3\}$ to …

2018年1月21日 · From wikipedia: "In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a discontinuous …

This section collects results on the discrete metric space. The discrete space is trivial and not very useful in applications. However, it helps clarify many of the theoretical underpinnings of the …

2015年10月12日 · In a discrete space, say a square/rectangular tiled space, (for convenience) we start by constructing two sides of a triangle, each of 1 unit length . To traverse the hypotenuse …

The power set P (X) of a non empty set X is called the discrete topology on X, and the space (X,P (X)) is called the discrete topological space or simply a discrete space. Now we shall show that …