  The concept of $typed$ $topology$ is introduced. In a typed topological
space, some open sets are assigned "types", and topological concepts such as
closure, connectedness can be defined using types. A finite data set in $R^2$
is a typically typed topological space. Clusters calculated by the DBSCAN
algorithm for data clustering can be well represent in a finite typed
topological space. Other concepts such as tracks, port (starting points),
type-p-connectedness, p-closure-connectedness, indexing, branches are also
introduced for a finite typed topological space. Finally, $left-r$ and
$up-left-r$ type open sets are introduced for data sets in $R^2$, so that
tracks, port, branches can be calculated.
