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  1. Region-based topology.Peter Roeper - 1997 - Journal of Philosophical Logic 26 (3):251-309.
    A topological description of space is given, based on the relation of connection among regions and the property of being limited. A minimal set of 10 constraints is shown to permit definitions of points and of open and closed sets of points and to be characteristic of locally compact T2 spaces. The effect of adding further constraints is investigated, especially those that characterise continua. Finally, the properties of mappings in region-based topology are studied. Not all such mappings correspond to point (...)
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  • Pieces of mereology.Andrzej Pietruszczak - 2005 - Logic and Logical Philosophy 14 (2):211-234.
    In this paper† we will treat mereology as a theory of some structures that are not axiomatizable in an elementary langauge and we will use a variable rangingover the power set of the universe of the structure). A mereological structure is an ordered pair M = hM,⊑i, where M is a non-empty set and ⊑is a binary relation in M, i.e., ⊑ is a subset of M × M. The relation ⊑ isa relation of being a mereological part . We (...)
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  • Connection structures.Loredana Biacino & Giangiacomo Gerla - 1991 - Notre Dame Journal of Formal Logic 32 (2):242-247.
    Whitehead, in his famous book "Process and Reality", proposed a definition of point assuming the concepts of “region” and “connection relation” as primitive. Several years after and independently Grzegorczyk, in a brief but very interesting paper proposed another definition of point in a system in which the inclusion relation and the relation of being separated were assumed as primitive. In this paper we compare their definitions and we show that, under rather natural assumptions, they coincide.
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  • Connection Structures: Grzegorczyk's and Whitehead's Definitions of Point.Loredana Biacino & Giangiacomo Gerla - 1996 - Notre Dame Journal of Formal Logic 37 (3):431-439.
    Whitehead, in his famous book Process and Reality, proposed a definition of point assuming the concepts of "region" and "connection relation" as primitive. Several years after and independently Grzegorczyk, in a brief but very interesting paper, proposed another definition of point in a system in which the inclusion relation and the relation of being separated were assumed as primitive. In this paper we compare their definitions and we show that, under rather natural assumptions, they coincide.
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  • Axiomatizability of geometry without points.Andrzej Grzegorczyk - 1960 - Synthese 12 (2-3):228 - 235.
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