A Hausdorff topological space X is called superconnected (resp. coregular ) if for any nonempty open sets U 1 , … n ⊆ the intersection of their closures ‾ ∩ not empty complement ∖ ( a regular space). canonical example projective Q P ∞ vector < ω = { x ∈ : | ≠ 0 } over field rationals . The quotient by equivalence relation ∼ y iff ⋅ We prove that every countable second-countable homeomorphic to ...

We investigate interpolation and extrapolation properties of composition-closed sets of partial operations defined on an infinite set E. Considering local completeness (interpolation property) the structure of a maximal local partial clone is described via its intersections with the full partial clones on every finite k-element (k 2) subset of E. The criteria are established which characterize ...

We study the extension of monadic second-order logic of order with cardinality quantifiers “there exists infinitely many sets” and “there exists uncountably many sets”. On linear orders that require the addition of only countably many points to be complete, we show using the composition method that the second-order uncountability quantifier can be reduced to the first-order uncountability quant...

We consider two relatively natural topologizations of the set of all cellular automata on a fixed alphabet. The first turns out to be rather pathological, in that the countable space becomes neither first-countable nor sequential. Also, reversible automata form a closed set, while surjective ones are dense. The second topology, which is induced by a metric, is studied in more detail. Continuity...

A space $Y$ is called an {em extension} of a space $X$, if $Y$ contains $X$ as a dense subspace. Two extensions of $X$ are said to be {em equivalent}, if there is a homeomorphism between them which fixes $X$ point-wise. For two (equivalence classes of) extensions $Y$ and $Y'$ of $X$ let $Yleq Y'$, if there is a continuous function of $Y'$ into $Y$ which fixes $X$ point-wise. An extension $Y$ ...

in this paper, countable compactness and the lindel¨of propertyare defined for l-fuzzy sets, where l is a complete de morgan algebra. theydon’t rely on the structure of the basis lattice l and no distributivity is requiredin l. a fuzzy compact l-set is countably compact and has the lindel¨ofproperty. an l-set having the lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

Currently, the most popular views about how to update de se or self-locating beliefs entail the one-third solution to the Sleeping Beauty problem. 2 Another widely held view is that an agent‘s credences should be countably additive. 3 In what follows, I will argue that there is a deep tension between these two positions. For the assumptions that underlie the one-third solution to the Sleeping B...