An open set is a set that, with every point P in it, contains all points of the metric space that are sufficiently near to P. |
| Открытое множество |  |
Откры́тое мно́жество — это множество, каждый элемент которого входит в него вместе с некоторой окрестностью. Например, внутренность шара является открытым множеством, а шар вместе с границей — не является открытым. Википедия
An open set of radius r and center x_0 is the set of all points x such that |x-x_0|<r, and is denoted D_r(x_0). In one-space, the open set is an open interval. |
An open set is a set that does not contain its boundary, in the same way that the endpoints of an interval are not contained in the interval. |
20 февр. 2017 г. · The idea of an open set is that for each point in the set, the set should also contain all other points that are sufficiently close to it. Or ... Helping provide intuition and clarity as to what exactly an "open ... What is an open set in a topological space? Другие результаты с сайта math.stackexchange.com |
If all the points in a set are interior points, meaning an open circle (or a bubble) can be drawn around them, then it is an open set. A set is closed if all ... |
In mathematics, fundamental topological property of sets that corresponds with the usual intuitive idea of having no breaks. |
A set A is an open set if, for every element x within the set (x∈A), there exists a neighborhood that still belongs to the set. |
(topology, mathematical analysis, restricted to metric spaces) A set which can be described as an (arbitrary) union of open balls. Equivalently, a set such that ... |
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