standard topology
In mathematics, 'standard topology' refers to the most commonly used topology on real numbers and Euclidean spaces, crucial for defining concepts like open sets and continuity.
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Definition
C2Real Analysis
(technical, academic)A topology on the set of real numbers where open sets are any unions of open intervals.
Example
- In the standard topology on the real numbers, an open interval like (0, 1) is considered an open set.
- The concept of continuity is defined using the standard topology on the real line.
C2Euclidean Space
(technical, academic)A topology on Euclidean space where open sets are any unions of open balls.
Example
- In the standard topology on \\(\mathbb{R}^2\\), an open ball is an open set.
- The standard topology on \\(\mathbb{R}^n\\) is fundamental in higher-dimensional analysis.
Similar
Terms that have similar or relatively close meanings to "standard topology":