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Consider three mutually tangent circles, and draw their inner Soddy circle. Then draw the inner Soddy circles of this circle with each pair of the original three, and ...

A recurrence equation (also called a difference equation) is the discrete analog of a differential equation. A difference equation involves an integer function f(n) in a form ...

A member of a collection of sets is said to be maximal if it cannot be expanded to another member by addition of any element. Maximal sets are important in graph theory since ...

A subset E of a topological space S is said to be nonmeager if E is of second category in S, i.e., if E cannot be written as the countable union of subsets which are nowhere ...

A subset S of a topological space X is compact if for every open cover of S there exists a finite subcover of S.

A subset A subset= X of a topological space X is said to be disconnected if it is not connected.

Three sets of three lines such that each line is incident with two from both other sets.

The Gosper island (Mandelbrot 1977), also known as a flowsnake (Gardner 1989, p. 41), is a fractal that is a modification of the Koch snowflake. The term "Gosper island" was ...

If F is a sigma-algebra and A is a subset of X, then A is called measurable if A is a member of F. X need not have, a priori, a topological structure. Even if it does, there ...

The study of definable sets and functions in polish spaces.