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In a complete metric space, a countable union of nowhere dense sets is said to be meager; the complement of such a set is a residual set.

A topological space is second countable if it has a countable topological basis.

A sigma-compact topological space is a topological space that is the union of countably many compact subsets.

The slope-intercept form of a line in the Cartesian plane is given by y=mx+b, where b is the y-intercept and m is the slope.

Find the tunnel between two points A and B on a gravitating sphere which gives the shortest transit time under the force of gravity. Assume the sphere to be nonrotating, of ...

A square grid is a grid formed by tiling the plane regularly with squares.

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.

A topological basis is a subset B of a set T in which all other open sets can be written as unions or finite intersections of B. For the real numbers, the set of all open ...

The closure of a set A is the smallest closed set containing A. Closed sets are closed under arbitrary intersection, so it is also the intersection of all closed sets ...

A function f is topologically transitive if, given any two intervals U and V, there is some positive integer k such that f^k(U) intersection V!=emptyset. Vaguely, this means ...