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In semi-algebraic geometry examples of open morphisms occur naturally, for example coverings. This paper emphasizes the investigation of open morphisms of locally semi-algebraic spaces from the point of view of real closed spaces. This means that real spectra and algebraic properties of rings of sections of locally semi-algebraic spaces play a role. Typical examples for results coming up in this context are the following: Open morphisms can be characterized in terms of a lifting property ofdoi:10.1016/0022-4049(88)90017-5 fatcat:eowcwojdg5e5tl4y7wmldwmenq