The 3 spatial dimensions and 1 time dimension are not continuous. If you were to consider a point infinitely far from the universe it can be considered to suffer none of the effects of relativity. No time dilation and no length contraction due to gravity. Every point from that position that is nearer to our universe would experience a degree of temporal slowing or physical contraction however infinitesimal. Another dimension can be considered this gradient of change with respect to gravitational sources.As a consequence of this the normal 3D geometry is altered or curved if you prefer, giving yet another dimension. Although these are not dimensions in the sense that we think of spacial direction they are still dimensional. As are fields, which are not visible to us.
When considering dimensions consider the following.
dimension
/dɪˈmɛnʃ(ə)n,dʌɪ-/
noun
noun: dimension; plural noun: dimensions
1.
a measurable extent of a particular kind, such as length, breadth, depth, or height.
"the final dimensions of the pond were 14 ft x 8 ft"synonyms: proportions, measurements, extent, size;
footage, acreage
"the approximate dimensions of the master bedroom"
a mode of linear extension of which there are three in space and two on a flat surface, which corresponds to one of a set of coordinates specifying the position of a point.
Physics
an expression for a derived physical quantity in terms of fundamental quantities such as mass, length, or time, raised to the appropriate power (acceleration, for example, having the dimension of length × time −2).
2.
an aspect or feature of a situation.
"we must focus on the cultural dimensions of the problem"synonyms: aspect, feature, element, facet, side