Scattered, Hausdorff-reducible, and hereditarily irresolvable spaces
نویسندگان
چکیده
منابع مشابه
Scattered, Hausdorff-reducible, and hereditarily irresolvable spaces
We show that a topological space is hereditarily irresolvable if and only if it is Hausdorff-reducible. We construct a compact irreducible T1-space and a connected Hausdorff space, each of which is strongly irresolvable. Furthermore, we show that the three notions of scattered, Hausdorff-reducible, and hereditarily irresolvable coincide for a large class of spaces, including metric, locally com...
متن کاملScattered and hereditarily irresolvable spaces in modal logic
When we interpret modal ♦ as the limit point operator of a topological space, the Gödel-Löb modal system GL defines the class Scat of scattered spaces. We give a partition of Scat into α-slices Sα , where α ranges over all ordinals. This provides topological completeness and definability results for extensions of GL. In particular, we axiomatize the modal logic of each ordinal α, thus obtaining...
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Several new characterizations of strongly irresolvable topological spaces are found and precise relationships are noted between strong irresolvability, hereditary irresolvability, and submaximality. It is noted that strong irresolvablity is a faint topological property, while neither hereditary irresolvablity nor submaximality are semitopological.
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For a topological space X, let L(X) be the modal logic of X where is interpreted as interior (and hence ♦ as closure) in X. It was shown in [6] that the modal logics S4, S4.1, S4.2, S4.1.2, S4.Grz, S4.Grzn (n ≥ 1), and their intersections arise as L(X) for some Stone space X. We give an example of a scattered Stone space whose logic is not such an intersection. This gives an affirmative answer ...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2003
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(03)00039-7