To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time. 4,5
Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Languages
Recent
Show all languages
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.
.
Leo
Newton
Brights
Milds # List of topologies

The following is a list of named topologies or topological spaces, many of which are counterexamples in topology and related branches of mathematics. This is not a list of properties that a topology or topological space might possess; for that, see List of general topology topics and Topological property.

## Widely known topologies

• The Baire space$\mathbb {N} ^{\mathbb {N} }$ with the product topology, where $\mathbb {N}$ denotes the natural numbers endowed with the discrete topology. It is the space of all sequences of natural numbers.
• Cantor set − A subset of the closed interval $[0,1]$ with remarkable properties.
• Discrete topology − All subsets are open.
• Euclidean topology − The natural topology on Euclidean space $\mathbb {R} ^{n}$ induced by the Euclidean metric, which is itself induced by the Euclidean norm.
• Indiscrete topology, chaotic topology, or Trivial topology − Only the empty set and its complement are open.
• Klein bottle
• Real projective line
• Torus

## Counter-example topologies

The following topologies are a known source of counterexamples for point-set topology.

## Topologies defined in terms of other topologies

### Natural topologies

List of natural topologies.

### Topologies of uniform convergence

This lists named topologies of uniform convergence.

### Other induced topologies

• Box topology
• Duplication of a point: Let $x\in X$ be a non-isolated point of $X,$ let $d\not \in X$ be arbitrary, and let $Y=X\cup \{d\}.$ Then $\tau =\{V\subseteq Y:{\text{ either }}V{\text{ or }}(V\setminus \{d\})\cup \{x\}{\text{ is an open subset of }}X\}$ is a topology on $Y$ and x and d have the same neighborhood filters in $Y.$ In this way, x has been duplicated.