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Space involves imagined area behind the surface of a painting.   Artists have almost always confronted the challenge of portraying a three-dimensional world on a two-dimensional surface.

Techniques employed to achieve an illusion of depth include:
size (objects...and the spaces between them...decrease as distance increases)
position (closer objects appear lower on the picture plane)
overlapping (object that are partially hidden must be behind)
foreshortening (shortening one dimension as a shape turns into the picture)
shading (surfaces appear darker as they turn away and reflect light less directly)
surface lines (curved lines drawn on a surface indicate a rounded surface)

Size sometimes takes the form of one- and two-point perspective.  The Italian Renaissance artists favored this approach since it appealed to their analytical outlook.

Color is sometimes used to indicate distance.  Cool colors (blue, etc.) tend to recede while warm colors (red, etc.)  advance.

Atmospheric conditions are also employed in creating depth.   Objects that are farther away appear to be less distinct and take on a bluer cast.   Artists from Northern Europe favored this approach to creating depth.

For more about dimension check Visual Literacy.
For more about perspective check Chalkboard.