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The space join of a topological space X and a pair of points S^0, Sigma(X)=X*S^0.

Sylvester's line problem, known as the Sylvester-Gallai theorem in proved form, states that it is not possible to arrange a finite number of points so that a line through ...

A symmetric design is a block design (v, k, lambda, r, b) with the same number of blocks as points, so b=v (or, equivalently, r=k). An example of a symmetric block design is ...

For any two points x,y in X, there is an open set U such that x in U and y not in U or y in U and x not in U. A space fulfilling this axiom is called a T0-space.

A topological space fulfilling the T0-separation axiom: For any two points x,y in X, there is an open set U such that x in U and y not in U or y in U and x not in U. ...

For any two points x,y in X there exists two open sets U and V such that x in U and y not in U, and y in V and x not in V. A space satisfying this axiom is known as a ...

Given any two distinct points x,y, there exist neighborhoods u and v of x and y, respectively, with u intersection v=emptyset. It then follows that finite subsets are closed.

Two circles with centers at (x_i,y_i) with radii r_i for i=1,2 are mutually tangent if (x_1-x_2)^2+(y_1-y_2)^2=(r_1+/-r_2)^2. (1) If the center of the second circle is inside ...

The planes passing through the vertices of a tetrahedron ABCD and tangent to the circumsphere at these points form another tetrahedron called the tangential tetrahedron. The ...

The set of all points x that can be put into one-to-one correspondence with sets of essentially distinct values of four homogeneous coordinates x_0:x_1:x_2:x_3, not all ...