Display case for preserving and displaying objects in a protected environment, comprising - a display space, delimited by separating walls comprising a lower plane and side walls, - means for adjusting and controlling air climate in the display space, such means comprising: - a hygrometric probe for detecting the relative humidity inside the display space, - a control unit, connected to the hygrometric probe, - a first relative humidity control electrolytic membrane, located in a first opening formed in one of the separating walls, activated by the control unit; - a second relative humidity control electrolytic membrane, located in a second opening formed in one of the separating walls and activated by the control unit, wherein the first electrolytic membrane is mounted in the first opening with a dry side thereof inwardly oriented in the display space while the second electrolytic membrane is mounted in the second opening with a humid side inwardly oriented in the display space; characterised in that the first electrolytic membrane and the second electrolytic membrane are alternatively activated by the control unit, for determined time ranges based on the relative humidity values detected by the hygrometric probe; and in that each of the two openings (51, 52) is provided with a shutter, movable between a closed position wherein it closes the opening (51, 52) when the electrolytic membrane (41, 42) in such opening is not activated and an open position wherein it leaves the opening (51, 52) open when the electrolytic membrane (41, 42) in such opening is activated. - a display space, delimited by separating walls comprising a lower plane and side walls, - means for adjusting and controlling air climate in the display space, such means comprising: - a hygrometric probe for detecting the relative humidity inside the display space, - a control unit, connected to the hygrometric probe, - a first relative humidity control electrolytic membrane, located in a first opening formed in one of the separating walls, activated by the control unit; - a second relative humidity control electrolytic membrane, located in a second opening formed in one of the separating walls and activated by the control unit, wherein the first electrolytic membrane is mounted in the first opening with a dry side thereof inwardly oriented in the display space while the second electrolytic membrane is mounted in the second opening with a humid side inwardly oriented in the display space; characterised in that the first electrolytic membrane and the second electrolytic membrane are alternatively activated by the control unit, for determined time ranges based on the relative humidity values detected by the hygrometric probe; and in that each of the two openings (51, 52) is provided with a shutter, movable between a closed position wherein it closes the opening (51, 52) when the electrolytic membrane (41, 42) in such opening is not activated and an open position wherein it leaves the opening (51, 52) open when the electrolytic membrane (41, 42) in such opening is activated. - a hygrometric probe for detecting the relative humidity inside the display space, - a control unit, connected to the hygrometric probe, - a first relative humidity control electrolytic membrane, located in a first opening formed in one of the separating walls, activated by the control unit; - a second relative humidity control electrolytic membrane, located in a second opening formed in one of the separating walls and activated by the control unit, wherein the first electrolytic membrane is mounted in the first opening with a dry side thereof inwardly oriented in the display space while the second electrolytic membrane is mounted in the second opening with a humid side inwardly oriented in the display space; characterised in that the first electrolytic membrane and the second electrolytic membrane are alternatively activated by the control unit, for determined time ranges based on the relative humidity values detected by the hygrometric probe; and in that each of the two openings (51, 52) is provided with a shutter, movable between a closed position wherein it closes the opening (51, 52) when the electrolytic membrane (41, 42) in such opening is not activated and an open position wherein it leaves the opening (51, 52) open when the electrolytic membrane (41, 42) in such opening is activated. wherein the first electrolytic membrane is mounted in the first opening with a dry side thereof inwardly oriented in the display space while the second electrolytic membrane is mounted in the second opening with a humid side inwardly oriented in the display space; characterised in that the first electrolytic membrane and the second electrolytic membrane are alternatively activated by the control unit, for determined time ranges based on the relative humidity values detected by the hygrometric probe; and in that each of the two openings (51, 52) is provided with a shutter, movable between a closed position wherein it closes the opening (51, 52) when the electrolytic membrane (41, 42) in such opening is not activated and an open position wherein it leaves the opening (51, 52) open when the electrolytic membrane (41, 42) in such opening is activated.