Editing String (computer science) (section)

=== Topology ===
[[File:Hamming distance 3 bit binary.svg|thumb|150px|(Hyper)cube of binary strings of length 3]]
Strings admit the following interpretation as nodes on a graph, where ''k'' is the number of symbols in Σ:
* Fixed-length strings of length ''n'' can be viewed as the integer locations in an ''n''-dimensional [[hypercube]] with sides of length ''k''-1.
* Variable-length strings (of finite length) can be viewed as nodes on a [[k-ary tree|perfect ''k''-ary tree]].
* [[Infinite string]]s (otherwise not considered here) can be viewed as infinite paths on a ''k''-node [[complete graph]].

The natural topology on the set of fixed-length strings or variable-length strings is the discrete topology, but the natural topology on the set of infinite strings is the [[limit topology]], viewing the set of infinite strings as the [[inverse limit]] of the sets of finite strings. This is the construction used for the [[p-adic|''p''-adic numbers]] and some constructions of the [[Cantor set]], and yields the same topology.

[[Isomorphism]]s between string representations of topologies can be found by normalizing according to the [[lexicographically minimal string rotation]].