Home > List of examples in general topology

• Alexandrov topology
• Cantor space
• Co-kappa topology
  • Cocountable topology
  • Cofinite topology
• Compact-open topology
• Compactification
• Discrete topology
• Extended real number line
• Hawaiian earring
• Hilbert cube
• Long line
• Order topology
  • Lexicographical/dictionary order
  • Ordinal number topologySet theory Ordinal numbers or ordinals for short, are numbers used to denote the position in an ordered sequence: first, second, third, fourth, etc. See How to name numbers''. In mathematics, ordinal numbers are an extension of the natural numbers to acco
  • Real lineIn mathematics, the real line is simply the set of real numbers. However, this term is usually used when R is to be treated as a space of some sort, such as a topological space or a vector space. The real line has been studied at least since the days of t
• Sierpinski spaceIn topology, Sierpinski space S is the simplest example of a topological space that does not satisfy the T axiom. It is useful as a counterexample and has many interesting properties related to general topological considerations. Definition Let S {0,1}.
• Sorgenfrey lineIn mathematics, the lower limit topology or right half-open interval topology is a topology defined on the set R of real numbers; it is different from the standard topology on R and has a number of interesting properties. It is the topology generated by t
• Sorgenfrey planeIn topology, the Sorgenfrey plane is a frequently-cited counterexample to many otherwise plausible-sounding conjectures. It consists of the product of two copies of the real line R under the half-open interval topology. A basis for the Sorgenfrey plane is
• Space-filling curveIntuitively, a "continuous curve" in the 2-dimensional plane or in the 3-dimensional space can be thought of as the "path of a continuously moving point". To eliminate the inherent vagueness of this notion, Jordan in 1887 introduced the following rigorous
• Topologist's sine curveIn the branch of mathematics known as topology, the topologist's sine curve is an example that has several interesting properties. It can be defined as a subset of the Euclidean plane as follows. Let S be the graph of the function sin(1/x) over the interv
• Trivial topologyIn topology, a topological space with the trivial topology is one where the only open sets are the empty set and the entire space. Such a space is sometimes called an indiscrete space . Intuitively, this has the consequence that all points of the space ar
• Unit interval
• Zariski topology