After Marie's latest addition of enriched spaces (and
some discussion
with Doug Arnold), it seems clear that our current
notation V + W for
mixed spaces is not optimal.
Even though one may think of the operation of creating a "mixed
function space" as a direct sum,
X = {(v, 0) : v in V} \oplus {(0, w) : w in W},
it is more natural (and common) to think of it as a
Cartesian product,
X = V \times W = {(v, w) : v in V, w in W}
It would therefore be more natural to use '*' instead of '+' as the
operation for creating mixed elements/function spaces.
That would free up '+' to be used for enriched spaces (which have
recently been added),
X = {v + w : v in V, w in W}
The typical example would be to take V piecewise
linears and W scaled
P3 bubbles.
In summary, the suggestion is to use the following notation:
+ <--> +
* <--> \times
It's obvious this is better than what we have now which is
+ <--> \oplus
? <--> +
Thoughts?
