Albert Einstein rather famously said
"The only reason for time is so that everything doesn't happen at once."
and John Wheeler added
"Space is what prevents everything from happening to me!"
I have noticed that everything doesn't happen at once and everything does not happen to me. Space and time have a real effect on me and so I believe they are real.
Without space there is no distance or volume. I no longer live 5 miles from work. I am already at work! And Thailand! And Alpha Centuri!!!
No such thing as space? I think thought has evolved since
http://plato.stanford.edu/entries/parmenides/
"The single known work of Parmenides is a poem which has survived only in fragmentary form, in which he argues that Reality is One, change is impossible, and that existence is timeless and uniform.'
FROM
https://en.wikiquote.org/wiki/Parmenides