Below left: Refinement of the cover so that no point in the shape is contained in more than 3 sets.
Below right: An attempt to refine the cover so that no point in the shape would be contained in more than 2 sets. Notice how some set border intersection points cannot be covered.
Purpose: To illustrate the role of covers in the definition of topological dimension, figure 2 of 2.
Licensing
Public domainPublic domainfalsefalse
This work has been released into the public domain by its author, Sigmundur. This applies worldwide.
In some countries this may not be legally possible; if so: Sigmundur grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.
(Above: Cover (four colourful sets) of a planar shape (dark).
Below left: Refinement of the cover so that no point in the shape is contained in more than 3 sets.
Below right: An attempt to refine the cover so that no point in the shape would be contained)
Captions
Add a one-line explanation of what this file represents