Ok regarding Measure Theory:

https://en.wikipedia.org/wiki/Measure_(mathematics)

From this article we can see that only zero, must remain without a length and width. It says nothing of dimension. Zero remains without a length and width.

Regarding Topology and set theory:

https://en.wikipedia.org/wiki/Zero-dimensional_space

This is a link referencing both:

At this point I must say...for this to continue in higher branches of mathematics a slight re-wording is required. But nothing else. We must say or allow that a "dimension" may exist abstractly...without a length and width. Further work of course is needed here.

So perhaps I was hasty to dismiss you on these two points Slip...but...one point is easily taken care of...the other should be also. More work to come.

https://en.wikipedia.org/wiki/Dimension

A bit late....but from this we can see...all I really need to do...is claim all "MY" spaces or... all dimensional unit quantities... are abstract....