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Separation axioms and frame representation of some topological facts

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Abstract

Similarly as the sobriety is essential for representing continuous maps as frame homo-morphisms, also other separation axioms play a basic role in expressing topological phenomena in frame language. In particular,T D is equivalent with the correctness of viewing subspaces as sublocates, or with representability of open or closed maps as open or closed homomorphisms. A weaker separation axiom is equivalent with an algebraic recognizability whether the intersection of a system of open sets remains open or not. The role of sobriety is also being analyzed in some detail.

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Authors and Affiliations

  1. Department of Applied Mathematics, MFF, Charles University, 11800, Praha 1, Czech Republic

    Aleš Pultr

  2. Dipartimento di Matematica Pura e Applicata, Università de L'Aquila, 67100, L'Aquila, Italy

    Anna Tozzi

Authors
  1. Aleš Pultr
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  2. Anna Tozzi
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In honour of Nico Pumplün on the occasion of his 60th birthday

The support of the Italian C.N.R. is gratefully acknowledged.

Partial financial support of the Italian M.U.R.S.T. is gratefully acknowledged.

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Pultr, A., Tozzi, A. Separation axioms and frame representation of some topological facts. Appl Categor Struct 2, 107–118 (1994). https://doi.org/10.1007/BF00878507

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