:Correction : " no distinction between inside and outside " means, according to the orientability article, that an " ant " crawling on one side at a particular spot can get to the other side of that same spot without leaving the surface or flipping over an edge.
32.
An important generalization of the notion of orientability of a space is that of orientability of a family of spaces parameterized by some other space ( a fiber bundle ) for which an orientation must be selected in each of the spaces which varies continuously with respect to changes in the parameter values.
33.
An important generalization of the notion of orientability of a space is that of orientability of a family of spaces parameterized by some other space ( a fiber bundle ) for which an orientation must be selected in each of the spaces which varies continuously with respect to changes in the parameter values.
34.
The significance of this construction begins with the following result, which belongs to the subject of cohomology of fiber bundles . ( We have stated the result in terms of "'Z "'2 coefficients to avoid complications arising from orientability; see also Orientation of a vector bundle # Thom space .)
35.
One feature of the bundle of densities ( again assuming orientability ) " L " is that " L " " s " is well-defined for real number values of " s "; this can be read from the transition functions, which take strictly positive real values.
