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Archive for Mathematical Logic
Original Item ID
Many properties of compacta have “textbook” definitions which are phrased in lattice-theoretic terms that, ostensibly, apply only to the full closed-set lattice of a space. We provide a simple criterion for identifying such definitions that may be paraphrased in terms that apply to all lattice bases of the space, thereby making model-theoretic tools available to study the defined properties. In this note we are primarily interested in properties of continua related to unicoherence; i.e., properties that speak to the existence of “holes” in a continuum and in certain of its subcontinua.
Bankston, Paul, "On the First-order Expressibility of Lattice Properties to Unicoherence in Continua" (2011). Mathematics, Statistics and Computer Science Faculty Research and Publications. 46.