Does the entropy of the space into which a star radiates (which has a temperature of about 3 k) increase or decrease? what does this do to the entropy of the universe?
To the best of our current knowledge, Universal entropy is ALWAYS increasing.
The radiation from a star increases the entropy of the star matter. The local region affected by the radiation may experience a decrease in entropy, such as element formation, but the NET entropy of the system is still increasing.