A display case for preserving and displaying objects in a protected environment. The display case includes: a display space, delimited by separating walls including a lower plane, side walls and a ceiling; and means for adjusting and controlling air climate in the display space. The means for adjusting and controlling include: a hygrometric probe for detecting the relative humidity inside the display space: a control unit, connected to the hygrometric probe and a first relative humidity control electrolytic membrane, located in a first opening formed in one of the separating walls, activated by the control unit.