A topological group is a group and topological space at the same time, where the group operations are required to be continuous.
A cantor set is given by taking the interval [0,1], removing the open middle third, removing the middle third of each of the two remaining pieces, and continuing this procedure ad infinitum.
August 2026
Any complex number has a 2x2 matrix representation. To be more precise, there is a ring homomorphism between a ring of matrices and the set of complex numbers.
Anticommutativity is a specific property of some noncommutative operations. Swapping the position of two arguments of an antisymmetric operation yields a result which is the inverse of the result with unswapped arguments.
Septemeber 2026
Number systems that involve complex numbers can be used to count the number of representations of an integer as the sum of two square integers.
The following statements are equivalent. For every nonempty set X there exists a binary operation * such that (X,*) is a group. The axiom of choice is true.