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A function f mapping a set X->X/R (X modulo R), where R is an equivalence relation in X, is called a canonical map.

The cardinal number of any set is lower than the cardinal number of the set of all its subsets. A corollary is that there is no highest aleph (aleph).

Every finite group of order n can be represented as a permutation group on n letters, as first proved by Cayley in 1878 (Rotman 1995).

The four following types of groups, 1. linear groups, 2. orthogonal groups, 3. symplectic groups, and 4. unitary groups, which were studied before more exotic types of groups ...

Cohomotopy groups are similar to homotopy groups. A cohomotopy group is a group related to the homotopy classes of maps from a space X into a sphere S^n.

Let L be a link in R^3 and let there be a disk D in the link complement R^3-L. Then a surface F such that D intersects F exactly in its boundary and its boundary does not ...

A theorem in set theory stating that, for all sets A and B, the following equivalences hold, A subset B<=>A intersection B=A<=>A union B=B.

A countable set is a set that is either finite or denumerable. However, some authors (e.g., Ciesielski 1997, p. 64) use the definition "equipollent to the finite ordinals," ...

The cubic groups are the point groups T_h and O_h together with their pure rotation subgroups T_d, T, and O (Cotton 1990, pp. 433-434).

A reciprocity theorem for the case n=3 solved by Gauss using "integers" of the form a+brho, when rho is a root of x^2+x+1=0 (i.e., rho equals -(-1)^(1/3) or (-1)^(2/3)) and ...