Space is basically uncountable (see this dictionary), thus mainly (2) in that context.
It can work as uncountable in circumstances where a certain area is dedicated to a purpose
The Kindergarten-primary Magazine - Volume 45 - Page 124 Bertha Johnston, E. Lyell Earle - 1932
For most schools, however, which close in June, and have a limited space for their gardens, the best vegetables to plant are radishes, beans, lettuce, chard and spinach.
but that usage is 10x less frequent at Google Books.