General topology

In mathematics a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence of elements of the space such that every nonempty open subset of the space contains at least one element of the sequence.

In mathematics, a direct limit (also called inductive limit) is a colimit of a "directed family of objects".

In mathematics, the closure of a subset S in a topological space consists of all points in S plus the limit points of S.

In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.

In topology, the exterior of a subset S of a topological space X is the union of all open sets of X which are disjoint from S.

In mathematics, the Sierpiński space (or the connected two-point set) is a finite topological space with two points, only one of which is closed.

In mathematical analysis, the intermediate value theorem states that if a continuous function, f, with an interval, [a, b], as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval.

In mathematics, the Hilbert cube, named after David Hilbert, is a topological space that provides an instructive example of some ideas in topology.

In mathematics, and especially general topology, the interlocking interval topology is an example of a topology on the set S := R+ \ Z+, i.

In topology, a clopen set (a portmanteau of closed-open set) in a topological space is a set which is both open and closed.

In mathematics, a cofinite subset of a set X is a subset A whose complement in X is a finite set.

This is a list of general topology topics, by Wikipedia page.

In mathematics, more specifically general topology, the double origin topology is an example of a topology given to the plane R2 with an extra point, say 0*, added.

In mathematics, a real-valued function or real function is a function whose values are real numbers.