If Y is a subset of X, X a totally ordered set, then Y inherits a total order from X. The set Y therefore has an order topology, … See more

Though the subspace topology of Y = {−1} ∪ {1/n }n∈N in the section above is shown not to be generated by the induced order on Y, it is nonetheless an order topology on Y; indeed, in the subspace topology every point is isol… See more

Several variants of the order topology can be given:
• The right order topology on X is the topology having as a base all intervals of the form , together with the set X.
• The left order topology o… See more

For any ordinal number λ one can consider the spaces of ordinal numbers
together with the natural order topology. These spaces are called ordinal spaces. (Note that in the usual set-theoretic constructio… See more

Any ordinal number can be viewed as a topological space by endowing it with the order topology (indeed, ordinals are well-ordered, so in particular totally ordered). Unless otherwise specified, this is the usual topology gi… See more

• List of topologies
• Lower limit topology
• Long line (topology)
• Linear continuum
• Order topology (functional analysis)… See more