Urban open spaces are considered as spatial residuals of the expansion of built areas. The environmental impact of the resulting land-cover pattern and associated ecosystem services are frequently evaluated at a crude spatial resolution only. However, wild animals use remaining interconnected fine-grain open spaces as an infrastructure for movement. In this paper, we traced the evolution of an open-space system in Haifa, Israel, and examined the impact of urban morphology on size and distribution of open spaces at different spatial resolutions. At a 30 m resolution, our analysis indicated fragmentation and increasing partial elimination of open spaces. Over time the connectivity declined at a diminishing rate, yet the network did not disintegrate into separate components. The evolution analysis implied that in crude resolution, the open space network is threatened. At a 5 m resolution, our analysis showed that Haifa remains porous to animal movement. Using combined multiple least-cost paths through the urban landscape of heterogeneous permeability, we illustrated extensive connectivity among open spaces. Backyards and other urban in-between spaces complemented the seminatural open-space network connectivity, enabling wildlife movement between habitat patches and thus survival in an urbanized environment.