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A topology defined on a totally ordered set X whose open sets are all the finite intersections of subsets of the form {x in X|x>a} or {x in X|x<a}, where a in X. The order ...

For some range of r, the Mandelbrot set lemniscate L_3 in the iteration towards the Mandelbrot set is a pear-shaped curve. In Cartesian coordinates with a constant r, the ...

Let f be a function defined on a set A and taking values in a set B. Then f is said to be a surjection (or surjective map) if, for any b in B, there exists an a in A for ...

Any set which can be put in a one-to-one correspondence with the natural numbers (or integers) so that a prescription can be given for identifying its members one at a time ...

A temporal point process is a random process whose realizations consist of the times {tau_j}_(j in J) of isolated events. Note that in some literature, the values tau_j are ...

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.

Greater than any assignable quantity of the sort in question. In mathematics, the concept of the infinite is made more precise through the notion of an infinite set.

Let R be a ring, and let I be an ideal of R. The correspondence A<->A/I is an inclusion preserving bijection between the set of subrings A of R that contain I and the set of ...

A balanced incomplete block design (B,V) is called resolvable if there exists a partition R of its set of blocks B into parallel classes, each of which in turn partitions the ...

Let L be a language of the first-order logic. Assume that the language L has the following sets of nonlogical symbols: 1. C is the set of constant symbols of L. (These are ...