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The Zariski topology is a topology that is well-suited for the study of polynomial equations in algebraic geometry, since a Zariski topology has many fewer open sets than in ...

Direct sums are defined for a number of different sorts of mathematical objects, including subspaces, matrices, modules, and groups. The matrix direct sum is defined by ...

The terms "measure," "measurable," etc. have very precise technical definitions (usually involving sigma-algebras) that can make them appear difficult to understand. However, ...

A weakened version of pointwise convergence hypothesis which states that, for X a measure space, f_n(x)->f(x) for all x in Y, where Y is a measurable subset of X such that ...

Let (X,tau) be a topological space, and let p in X. Then the arc component of p is union {A subset= X:A is an arc and p in A}.

A basepoint is the beginning and ending point of a loop. The fundamental group of a topological space is always with respect to a particular choice of basepoint.

A subset X subset Y is said to be bicollared in Y if there exists an embedding b:X×[-1,1]->Y such that b(x,0)=x when x in X. The map b or its image is then said to be the ...

If F is the Borel sigma-algebra on some topological space, then a measure m:F->R is said to be a Borel measure (or Borel probability measure). For a Borel measure, all ...

The points on a line can be put into a one-to-one correspondence with the real numbers.

omega^epsilon=epsilon, where omega is an ordinal number and epsilon is an inaccessible cardinal.