In a globalized society, which declared crossing the border as a positive act, space seems to play only a marginal role. The aim is to reduce distances and let them disappear. Space shrinks to a constantly determining size. Distance plays only a minor role in the specific processes of global society. However, despite many transnational tendencies space is not a meaningless subject. New Media forms an information society which is characterized by an excess of space. The cyberspace plays a significant role for this boundless society. Space must therefore be completely rethought and differentiated in the age of globalization. Instead of a completely unlimited world new borders are created.The former clear dividing line is transformed into a new wider area. A society raises, in which people are confronted with reappearance and disapperance of space and borders.