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An algebra <L; ^ , v > is called a lattice if L is a nonempty set, ^ and v are binary operations on L, both ^ and v are idempotent, commutative, and associative, and they ...

A totally disconnected space is a space in which all subsets with more than one element are disconnected. In particular, if it has more than one element, it is a disconnected ...

In a lattice, any two elements a and b have a least upper bound. This least upper bound is often called the join of a and b, and is denoted by a v b. One can also speak of ...

In a lattice, any two elements a and b have a greatest lower bound. This greatest lower bound is often called the meet of a and b, and is denoted by a ^ b. One can also speak ...

An "area" which can be defined for every set--even those without a true geometric area--which is rigid and finitely additive.

S_n=sum_(i)eta_imu(E_i), where mu(E_i) is the measure of the set E_i of points on the x-axis for which f(x) approx eta_i.

An integer that is either 0 or positive, i.e., a member of the set Z^*={0} union Z^+, where Z-+ denotes the positive integers.

An integer that is either 0 or negative, i.e., a member of the set {0} union Z^-, where Z-- denotes the negative integers.

A monotonic function is a function which is either entirely nonincreasing or nondecreasing. A function is monotonic if its first derivative (which need not be continuous) ...

The supremum is the least upper bound of a set S, defined as a quantity M such that no member of the set exceeds M, but if epsilon is any positive quantity, however small, ...