Hi Aleksandr,
You say 'time acts throughout space' but, IMO, that's not quite the right expression. Energy acts, time applies It is more like labelling ,identifying. lets say you have as far as you can tell a complexly empty volume of space. Nothing to identify it from any other similar volume. Now imagine you can see a dot, which divides into two ,then 4 dots. Now there was a time of 1 dot followed by a time of 2 dots followed by a time of 4 dots, The time pertains to the existence in the space, its distribution and arrangement are useful descriptors. The sequence of the dots gives the 'direction' of the arrow of time.