What is the purpose of this map?

The map is clearly titled "City of Cape Town Population Map". The legend provides a classification of population numbers, with different shades of color corresponding to specific population ranges (e.g., $0-43369$, $43369-86738$, up to $390319-433688$). This directly indicates that the map's subject is population.

Option "a. To indicate available unoccupied spaces in and around" suggests the map is about empty or undeveloped land. This contradicts the map's title and legend, which are focused on population figures, not land availability or occupancy status.

Based on the title and legend, the map's purpose is to visually represent how population is distributed across different areas of the City of Cape Town, highlighting areas with higher or lower population densities.

Therefore, option 'a' is incorrect. The map's purpose is to show population distribution.