-biČech spaces and -biČech spaces.
-spaces and -spaces.
-minimal subsets of the circle
Necessary conditions are found for a Cantor subset of the circle to be minimal for some -diffeomorphism. These conditions are not satisfied by the usual ternary Cantor set.
weakly chaotic functions with zero topological entropy and non- flat critical points.
C- and C*-quotients in pointfree topology [Book]
-compactness modulo an ideal.
-continuity and closed graphs
is not subsequential
If a separable dense in itself metric space is not a union of countably many nowhere dense subsets, then its -space is not subsequential.
-Movably regular convergences
-points vs -points and -points
In a Tychonoff space , the point is called a -point if every real-valued continuous function on can be extended continuously to . Every point in an extremally disconnected space is a -point. A classic example is the space consisting of the countable ordinals together with . The point is known to be a -point as well as a -point. We supply a characterization of -points in totally ordered spaces. The remainder of our time is aimed at studying when a point in a product space is a -point....
-commuting maps and invariant approximations.
-spaces and simplicial complexes.
can sometimes determine without being realcompact
As usual will denote the ring of real-valued continuous functions on a Tychonoff space . It is well-known that if and are realcompact spaces such that and are isomorphic, then and are homeomorphic; that is determines. The restriction to realcompact spaces stems from the fact that and are isomorphic, where is the (Hewitt) realcompactification of . In this note, a class of locally compact spaces that includes properly the class of locally compact realcompact spaces is exhibited...
in the weak topology.
Calculation of the free energy in a simple model
Caliber (, ω) is not productive
Calibres, compacta and diagonals
For a space Z let 𝒦(Z) denote the partially ordered set of all compact subspaces of Z under set inclusion. If X is a compact space, Δ is the diagonal in X², and 𝒦(X²∖Δ) has calibre (ω₁,ω), then X is metrizable. There is a compact space X such that X²∖Δ has relative calibre (ω₁,ω) in 𝒦(X²∖Δ), but which is not metrizable. Questions of Cascales et al. (2011) concerning order constraints on 𝒦(A) for every subspace of a space X are answered.
Can we assign the Borel hulls in a monotone way?
A hull of A ⊆ [0,1] is a set H containing A such that λ*(H) = λ*(A). We investigate all four versions of the following problem. Does there exist a monotone (with respect to inclusion) map that assigns a Borel/ hull to every negligible/measurable subset of [0,1]? Three versions turn out to be independent of ZFC, while in the fourth case we only prove that the nonexistence of a monotone hull operation for all measurable sets is consistent. It remains open whether existence here is also consistent....
Canonical and op-canonical lax algebras.
Canonical embedding of function spaces into the topological bidual of .