It's sort of possible, with a large enough sensor and good enough optics.
There are at least two compacts on the market that fit the bill:
- Fuji X100S with an APS-C sensor. That's the same sensor size as low- to mid-end DSLRs.
- Sony RX1 with a full frame sensor, same as high-end/pro DSLRs. (The price tag is also in the high-end DSLR region.)
Both of these have fixed lenses, no zoom. The problem with adding a fast, high-quality zoom to a large-sensor compact is that the lens will be so large that it's hardly "compact" anymore.
With a fixed lens, these compacts produce pictures with quality comparable to a DSRL, but only in a relatively narrow range of scenarios: They can compete with DSLRs for street photography, for instance, but can't compete for ultra-wide-angle shots or sports/birds/wildlife, where the DSLR user can switch lenses to adapt.
If you want zoom, I think a mirrorless is your best bet. The large-sensor mirrorless (APS-C, and micro-four-thirds isn't too far off) aren't as compact as the compacts, mostly because of the lenses. But they are still more compact than DSLRs, and offer interchangeable lenses.
For keywords, I would try "large sensor compact", just be aware that some of the hits will be for sensors that are large for a compact, but still small compared to a DSLR.