Category:Definitions/Generalized Ordered Spaces

This category contains definitions related to Generalized Ordered Spaces.
Related results can be found in Category:Generalized Ordered Spaces.

$\struct {S, \preceq, \tau}$ is a generalized ordered space if and only if:

$(1): \quad \struct {S, \tau}$ is a Hausdorff space

$(2): \quad$ there exists a basis for $\struct {S, \tau}$ whose elements are convex in $S$.