If and this limit is unique (i.e. only for ) then one writes:using the equal sign in place of the arrow In a Hausdorff space, every net has at most one limit, and the limit of a convergent net is always unique. Some authors do not distinguish between the notations and , but this can lead to ambiguities if the ambient space is not Hausdorff.
If and this limit is unique (i.e. only for ) then one writes:using the equal sign in place of the arrow In a Hausdorff space, every net has at most one limit, and the limit of a convergent net is always unique. Some authors do not distinguish between the notations and , but this can lead to ambiguities if the ambient space is not Hausdorff