Notes on characterization of paracompact frames
On models in the alternative set theory
On the Continuity of Internal Functions
On the paracompactness of frames
Through the study of frame congruences, new characterizations of the paracompactness of frames are obtained.
On the thickness of topological spaces
Realcompactification of frames
We give a construction of Wallman-type realcompactifications of a frame by considering regular sub -frames the join of which generates . In particular, we show that the largest such regular sub -frame gives rise to the universal realcompactification of .
Relationship among various Vietoris-type and microsimplicial homology theories
In this paper, we clarify the relationship among the Vietoris-type homology theories and the microsimplicial homology theories, where the latter are nonstandard homology theories defined by M.C. McCord (for topological spaces), T. Korppi (for completely regular topological spaces) and the author (for uniform spaces). We show that McCord’s and our homology are isomorphic for all compact uniform spaces and that Korppi’s and our homology are isomorphic for all fine uniform spaces. Our homology shares...
Simple motions
Some applications of non-standard analysis to proximity spaces
Some connections between measure, indiscernibility and representation of cuts
The notions of w-net and Y-compact space viewed under infinitesimal microscope.
Théorème d'Ascoli et application aux groupes topologiques localement compacts en analyse non standard
Topological properties of the real numbers object in a topos
Translation of nonstandard definitions to standard ones
Two Examples of Q-topologies
Two examples of Q-topologies.
Ultrafilter spaces and compactifications.
Ultrametrics and infinite dimensional whitehead theorems in shape theory.
Une approche non-standard de la dimension d'un espace topologique
Une théorie générale des infinitésimaux