Articles by Author: Ale Pultr

Search results for Ale Pultr

We found 12 results for you
  1. Ideals in Heyting Semilattices and Open Homomorphisms

    Ideals in Heyting Semilattices and Open Homomorphisms

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    Subfitness and its relation to openness and completeness is studied in the context of Heyting semilattices. A formally weaker condition (c-subfitness) is shown to be necessary and sufficient for openness and completeness to coincide. For a large class of spatial...
  2. Homomorphisms of complete distributive lattices

    Homomorphisms of complete distributive lattices

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    The category of all complete distributive lattices and their complete homomorphisms is universal, and this is also true for the category of all complete distributive lattices whose morphisms preserve complete joins, finite meets and an additional nullary operation. A survey...
  3. Extremal Prime Filters and Universality of Some Categories

    Extremal Prime Filters and Universality of Some Categories

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    Due to the existence of constants, classical topological categories cannot be universal in the sense of containing each concrete category as a full subcategory. In the point-free case, this obstruction vanishes and the question of universality makes sense again. The...
  4. CAUCHY POINTS OF UNIFORM AND NEARNESS FRAMES

    CAUCHY POINTS OF UNIFORM AND NEARNESS FRAMES

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    The notion of Cauchy point (= regular Cauchy filter) and the corresponding Cauchy spectrum, for a nearness frame (= uniform without the star-refinement condition) are investigated in various directions, including basic motivation, several functorial aspects, and the recognition of the...
  5. ON THE COMPLETION OF NEARNESS FRAMES

    ON THE COMPLETION OF NEARNESS FRAMES

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    Several questions naturally arising from the unique existence of the completion of a nearness frame are investigated. In particular, the classical result that completion is a coreflection for uniform frames is extended to a substantially larger class of nearness frames...
  6. A NOTE ON RECONSTRUCTION OF SPACES AND MAPS FROM LATTICE DATA

    A NOTE ON RECONSTRUCTION OF SPACES AND MAPS FROM LATTICE DATA

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    Reconstruction of topological spaces from the lattices Ω(X) of open sets, and of continuous maps from lattice homomorphisms satisfying additional properties (formulated in lattice terms) is discussed. We focus on the question when and how the filters λ(x) = {U...
  7. Pointfree Aspects of the <em>T<sub>d</sub>
               </em> Axiom of Classical Topology

    Pointfree Aspects of the <em>T<sub>d</sub> </em> Axiom of Classical Topology

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    Abstraction from the condition defining To-spaces leads to the following notion in an arbitrary frame L: a filter F in L is called slicing if it is prime and there exist a, b e L such that a £ F,...
  8. Epimorphisms of metric frames

    Epimorphisms of metric frames

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    This paper deals with several aspects of epimorphisms in the category MFrm of metric frames and contractive homomorphisms. In particular, it is shown that i. the epicomplete metric frames are uniquely determined by the power-set lattices of sets,...
  9. On covered prime elements and complete homomorphisms of frames

    On covered prime elements and complete homomorphisms of frames

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    It is a standard fact that the right adjoints h* of general frame homomor- phisms h : L → M send prime elements to prime elements. Unlike this, the preservation of covered prime elements by complete frame homomorphism is a...
  10. Tightness relative to some (co)reflections in topology

    Tightness relative to some (co)reflections in topology

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    We address what might be termed the reverse reflection problem: given a monoreflection from a category A onto a subcategory B, when is a given object B ∈ B the reflection of a proper subobject? We start with a well...