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19:3919:39, 12 June 2026 Metric (hist | edit) [7,520 bytes] InfernalAtom683 (talk | contribs) (Created page with "In mathematics, a '''metric''' or '''distance function''' is a function that defines a rigorous concept of distance between each pair of elements in a given set. By generalizing the physical concept of distance, metrics allow mathematicians to define topological concepts such as open and closed sets, continuity, convergence, and limits in highly abstract spaces. A set equipped with a metric is called a metric sp...") Tag: Visual edit

22:5322:53, 11 June 2026 Ring (hist | edit) [808 bytes] InfernalAtom683 (talk | contribs) (Created page with "In ring theory, a **ring** is an algebraic sturcture consisting of a set with two binary operations. Integer equiped with addition and multiplication, polinomials, square matrices and functions are typical examples of rings. ==Definition== Suppose that <math>R</math> is a set and <math>+, \cdot\colon R\times R \to R</math> are two binary operations on <math>R</math>. The ordered triplet <math>(R,+,\cdot)</math> is a ring if it satisfies: # <math>(R,+)</math> is...") Tag: Visual edit

15:3715:37, 14 May 2026 Seifert-Van Kampen theorem (hist | edit) [1,018 bytes] InfernalAtom683 (talk | contribs) (Created page with "== Statement == Let <math>X</math> be a topological space, and <math>U, V\subset X</math> be open sets such that <math>X = U\cup V</math>, and <math>U</math>, <math>V</math> and <math>U\cap V</math> are path-connected. Take a basepoint <math>x_0\in U\cap V</math> with inclusion maps: <math display="block">i\colon U\cap V\hookrightarrow U,\quad j\colon U\cap V\hookrightarrow V,\quad k\colon U\hookrightarrow X,\quad l\colon V\hookrightarrow X,</math> then the following d...") Tag: Visual edit: Switched

21:5721:57, 29 April 2026 Commutator (hist | edit) [4,305 bytes] InfernalAtom683 (talk | contribs) (Created page with "A '''commutator''' is an algebraic expression that measures the failure of two elements to commute. It occurs throughout abstract algebra, particularly in group theory, ring theory, and linear algebra. If two elements commute, their commutator is trivial. More generally, the commutator describes the obstruction to exchanging the order of two operations. Commutators are fundamental in the study of noncommutative structures and in the construction of i...")