In mathematics, general topology (or point set topology) is the branch of topology that deals with the basic set-theoretic definitions and constructions...

of topology, including differential topology, geometric topology, and algebraic topology. Another name for general topology is point-set topology. The...

In mathematics, weak topology is an alternative term for certain initial topologies, often on topological vector spaces or spaces of linear operators,...

of topological spaces in their own right is called point-set topology or general topology. Around 1735, Leonhard Euler discovered the formula V − E + F...

In topology and related areas of mathematics, the quotient space of a topological space under a given equivalence relation is a new topological space constructed...

areas of topology, the focus here is on general topology. The following definitions are also fundamental to algebraic topology, differential topology and geometric...

In mathematics, specifically in topology, the interior of a subset S of a topological space X is the union of all subsets of S that are open in X. A point...

its elements is an open set. Covers are commonly used in the context of topology. If the set X {\displaystyle X} is a topological space, then a cover C...

examples in general topology, a field of mathematics. Alexandrov topology Cantor space Co-kappa topology Cocountable topology Cofinite topology Compact-open...

natural topology called the product topology. This topology differs from another, perhaps more natural-seeming, topology called the box topology, which...

mathematics, an order topology is a specific topology that can be defined on any totally ordered set. It is a natural generalization of the topology of the real...

In topology, the closure of a subset S of points in a topological space consists of all points in S together with all limit points of S. The closure of...

In topology and related areas of mathematics, the set of all possible topologies on a given set forms a partially ordered set. This order relation can...

topology τ of a topological space (X, τ) is a family B {\displaystyle {\mathcal {B}}} of open subsets of X such that every open set of the topology is...

from that of X called the subspace topology (or the relative topology, or the induced topology, or the trace topology).[citation needed] Given a topological...

In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean...

In topology and mathematics in general, the boundary of a subset S of a topological space X is the set of points in the closure of S not belonging to...

In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space. It is closely related...

In topology and related branches of mathematics, a Hausdorff space (/ˈhaʊsdɔːrf/ HOWSS-dorf, /ˈhaʊzdɔːrf/ HOWZ-dorf), separated space or T2 space is a...

In topology and related areas of mathematics, a subset A of a topological space X is said to be dense in X if every point of X either belongs to A or else...

list of general topology topics. Topological space Topological property Open set, closed set Clopen set Closure (topology) Boundary (topology) Dense (topology)...

that a topology or topological space might possess; for that, see List of general topology topics and Topological property. Discrete topology − All subsets...

distance is defined in general. Less intuitive topologies are used in other branches of mathematics; for example, the Zariski topology, which is fundamental...

In mathematics, and especially general topology, the Euclidean topology is the natural topology induced on n {\displaystyle n} -dimensional Euclidean space...

In general topology and related areas of mathematics, the final topology (or coinduced, strong, colimit, or inductive topology) on a set X , {\displaystyle...

In mathematics, the lower limit topology or right half-open interval topology is a topology defined on R {\displaystyle \mathbb {R} } , the set of real...

{\displaystyle Y} , so that X ⊆ Y {\displaystyle X\subseteq Y} . In general topology, an embedding is a homeomorphism onto its image. More explicitly, an...

Connected and disconnected subspaces of R² In topology and related branches of mathematics, a connected space is a topological space that cannot be represented...

topology, the cartesian product of topological spaces can be given several different topologies. One of the more natural choices is the box topology,...

In general topology and related areas of mathematics, the initial topology (or induced topology or weak topology or limit topology or projective topology)...