Voltage-controlled resistive switching in various gap systems on SiO2 substrates is demonstrated. The nanosized gaps are made by several means using different materials including metals, semiconductors and amorphous carbon. The switching site is further reduced in size by using multi-walled carbon nanotubes and single-walled carbon nanotubes. The switching in all the gap systems shares the same characteristics. This independence of switching on the material compositions of the electrodes, accompanied by observable damage to the SiO2 substrate at the gap region, bespeaks the intrinsic switching from post-breakdown SiO2. It calls for caution when studying resistive switching in nanosystems on oxide substrates, since oxide breakdown extrinsic to the nanosystem can mimic resistive switching. Meanwhile, the devices show promising memory properties. The observed intermediate states reveal the filamentary nature of the switching. The switching is further explored in a vertical representation as potential candidate for high-density memory applications.