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On some topological concepts via the lattice of closed sets

  • Autores: M. N. Mukherjee, A. Sengupta
  • Localización: Revista de la Academia Canaria de Ciencias: = Folia Canariensis Academiae Scientiarum, ISSN 1130-4723, Vol. 16, Nº. 1-2, 2004, págs. 57-69
  • Idioma: inglés
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  • Resumen
    • The paper is devoted chiefly to the study of t he interplay between certain topological concepts of a topological space X and sorne lattice concepts of L(X)-the lattice of closed subsets of X under set inclusion . Among other things, the notions of connectedness of a topological space and homeomorphism between two spaces have been characterized in the language of lattices. Moreover, we introduce sorne separation-like properties of a bounded distributive lattice, and investigate the interrelations between these properties applied to L(X) and sorne separation axioms like Hausdorffness and normali ty of a topological space X. Lastly, an equivalent description of the notion of dimension of a topological space X is achieved in terms of a lattice theoretic concept, introduced suita bly.


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