  Short-GRB progenitors could come in various flavors, depending on the nature
of the merging compact stellar objects (including a stellar-mass black hole or
not) or depending on their ages (millions or billions of years). At a redshift
of z=0.122, the nearly face-on spiral host of the short GRB 080905A is one of
the closest short-GRB host galaxies identified so far. This made it a preferred
target to explore spatially resolved star-formation and to investigate the
afterglow position in the context of its star formation structures. We used
VLT/MUSE integral-field unit observations, supplemented by ATCA 5.5/9.0 GHz
radio-continuum measurements and publicly available HST data, to study the
star-formation activity in the GRB 080905A host galaxy. The MUSE observations
reveal that the entire host is characterized by strong line emission. Using the
Halpha line flux, we measure for the entire galaxy an SFR of about 1.6 Msun/yr,
consistent with its non-detection by ATCA. Several individual star-forming
regions are scattered across the host. The most luminous region has a Halpha
luminosity that is nearly four times as high as the luminosity of the Tarantula
nebula in the Large Magellanic Cloud. Even though star-forming activity can be
traced as close to about 3 kpc (in projection) distance to the GRB explosion
site, stellar population synthesis calculations show that none of the
Halpha-bright star-forming regions is a likely birthplace of the short-GRB
progenitor.
