In the quest for post-CMOS (complementary metal-oxide-semiconductor) technologies, driven by the need for improved efficiency and performance, topologically protected ferromagnetic 'whirls' such as skyrmions(1-8) and their anti-particles have shown great promise as solitonic information carriers in racetrack memory-in-logic or neuromorphic devices(1,9-11). However, the presence of dipolar fields in ferromagnets, which restricts the formation of ultrasmall topological textures(3,6,8,9,12), and the deleterious skyrmion Hall effect, when skyrmions are driven by spin torques(9,10,12), have thus far inhibited their practical implementation. Antiferromagnetic analogues, which are predicted to demonstrate relativistic dynamics, fast deflection-free motion and size scaling, have recently become the subject of intense focus(9,13-19), but they have yet to be experimentally demonstrated in natural antiferromagnetic systems. Here we realize a family of topological antiferromagnetic spin textures in alpha-Fe2O3-an Earth-abundant oxide insulator-capped with a platinum overlayer. By exploiting a first-order analogue of the Kibble-Zurek mechanism(20,21), we stabilize exotic merons and antimerons (half-skyrmions)(8) and their pairs (bimerons)(16,22), which can be erased by magnetic fields and regenerated by temperature cycling. These structures have characteristic sizes of the order of 100 nanometres and can be chemically controlled via precise tuning of the exchange and anisotropy, with pathways through which further scaling may be achieved. Driven by current-based spin torques from the heavy-metal overlayer, some of these antiferromagnetic textures could emerge as prime candidates for low-energy antiferromagnetic spintronics at room temperature(1,9-11,23).