In mathematics, the excluded point topology is a topology where exclusion of a particular point defines openness. Formally, let X be any non-empty set...

has a single point, X ∗ {\displaystyle X^{*}} is ultraconnected. For a set Z and a point p in Z, one obtains the excluded point topology construction...

extension topology Finite excluded point topology Countable excluded point topology Uncountable excluded point topology Open extension topology Either-or...

infinity is the accumulation point; (2) a space with the excluded point topology, where the "excluded point" is the accumulation point. Every Hausdorff door...

particular point topology on the set {0,1}. The excluded point topology on any set with at least two elements is T0 but not T1. The only closed point is the...

general topology (or point set topology) is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It...

space X. For example, the particular point topology on a finite space is hyperconnected while the excluded point topology is ultraconnected. The Sierpiński...

mathematics, the particular point topology (or included point topology) is a topology where a set is open if it contains a particular point of the topological...

senses (1), (2) and (3), but not (4) or (5). More generally, the excluded point topology is locally compact in senses (1), (2) and (3), and compact, but...

both the finite particular point topology (with particular point 1) and the finite excluded point topology (with excluded point 0). Therefore, S {\displaystyle...

indiscrete topology. The Sierpiński space. A set with the excluded point topology. The right order topology on the real line. Hyperconnected space PlanetMath...

Comb space Dieudonné plank Double origin topology Dunce hat (topology) Either–or topology Excluded point topology − A topological space where the open sets...

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

connected if it is connected under its subspace topology. Some authors exclude the empty set (with its unique topology) as a connected space, but this article...

he is known as one of the founders of modern topology, particularly for establishing his fixed-point theorem and the topological invariance of dimension...

have a rich set of invariants, coming from point-set topology, classic algebraic topology, and geometric topology. The most familiar invariants, which are...

this set, Cantor and others helped lay the foundations of modern point-set topology. The most common construction is the Cantor ternary set, built by...

mathematics, the Schoenflies problem or Schoenflies theorem, of geometric topology is a sharpening of the Jordan curve theorem by Arthur Schoenflies. For...

for the case in which it is excluded. A topology on X {\displaystyle X} defines a notion of a filter converging to a point x {\displaystyle x} of X , {\displaystyle...

standard topology, Euclidean topology, or usual topology) can be obtained not only from Cartesian product. It is also identical to the natural topology induced...

topology by carefully selecting the members of the class. If a student had already studied topology elsewhere or had read too much, he would exclude him...

The open intervals are those intervals that are open sets for the usual topology on the real numbers. A closed interval is an interval that includes all...

authors, especially those interested in applications to algebraic topology, explicitly exclude the empty set from being irreducible. This article will not follow...

Dolecki, Szymon; Mynard, Frédéric (2016). Convergence Foundations of Topology. Hackensack, New Jersey: World Scientific Publishing. pp. 27–54. doi:10...

PSTN network topology is the switching network topology of a telephone network connected to the public switched telephone network (PSTN). In the United...

while, in topology and differential geometry, it may not. A surface is a topological space of dimension two; this means that a moving point on a surface...

Horizontal cross-connects provide a point for the consolidation of all horizontal cabling, which extends in a star topology to individual work areas such as...

In general topology, set theory and game theory, a Banach–Mazur game is a topological game played by two players, trying to pin down elements in a set...

the real numbers inherit a metric topology from the metric defined above. The order topology and metric topology on R are the same. As a topological...

origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology) and abstract algebra (theory of modules and syzygies)...