  Peirce also made a number of remarks that suggest, in connection with the foregoing enterprise, that he had a novel conception of the topology of points in a continuum. All these remarks he connected with his previous defenses of infinite sets. For these reasons some Peirce scholars, and in particular the great Peirce scholar Carolyn Eisele, have suggested that his ideas were an anticipation of Abraham Robinson’s non-standard analysis of 1964. Whether this actually be so or not, however, is at the present time far from clear. Peirce certainly says many things that are quite suggestive of the construction of non-standard models of the theory of ordered fields by means of using equivalence classes of countably infinite Cartesian Products of the standard real numbers and then applying Loś’s Theorem. However, no commentator up to now has provided anything even remotely resembling a careful and detailed exposition of Peirce’s thinking in this area. Unfortunately, most of Peirce’s published writing and public talks on this topic were designed for audiences that were extremely unsophisticated mathematically (a fact that he lamented).  For that reason most of what Peirce said on the topic is picturesque and intriguing, but extremely obscure. The entire analysis of Peirce’s notion of an infinitesimal, as well as the exact bearing this notion has on his concept of a real continuum and on his idea of the topology of the points of a continuum, still awaits meticulous mathematical discussion.