Collectionwise Hausdorff property in product spaces
Compact and extremally disconnected spaces.
Compact scattered spaces in forcing extensions
We consider the cardinal sequences of compact scattered spaces in models where CH is false. We describe a number of models of in which no such space can have ℵ₂ countable levels.
Compact sets without converging sequences in the random real model.
Compactifications, and ring epimorphisms.
Compactness of the hyperplane topology
Complete -bounded groups need not be -factorizable
We present an example of a complete -bounded topological group which is not -factorizable. In addition, every -set in the group is open, but is not Lindelöf.
Completely regular modification and products
Completely regular spaces
We conduct an investigation of the relationships which exist between various generalizations of complete regularity in the setting of merotopic spaces, with particular attention to filter spaces such as Cauchy spaces and convergence spaces. Our primary contribution consists in the presentation of several counterexamples establishing the divergence of various such generalizations of complete regularity. We give examples of: (1) a contigual zero space which is not weakly regular and is not a Cauchy...
Completeness and Fixed-Points.
Completeness properties of function rings in pointfree topology
This note establishes that the familiar internal characterizations of the Tychonoff spaces whose rings of continuous real-valued functions are complete, or -complete, as lattice ordered rings already hold in the larger setting of pointfree topology. In addition, we prove the corresponding results for rings of integer-valued functions.
Concerning cut point spaces of order three.
Concerning the structure of dendritic spaces
Connected economically metrizable spaces
A topological space is non-separably connected if it is connected but all of its connected separable subspaces are singletons. We show that each connected sequential topological space X is the image of a non-separably connected complete metric space X under a monotone quotient map. The metric of the space X is economical in the sense that for each infinite subspace A ⊂ X the cardinality of the set does not exceed the density of A, . The construction of the space X determines a functor : Top...
Constructions of thin-tall Boolean spaces.
This is an expository paper about constructions of locally compact, Hausdorff, scattered spaces whose Cantor-Bendixson height has cardinality greater than their Cantor-Bendixson width.
Containing spaces for planar rational compacta [Book]
Continuous images of which are homeomorphic to .
Continuous pseudo-hairy spaces and continuous pseudo-fans
A compact metric space X̃ is said to be a continuous pseudo-hairy space over a compact space X ⊂ X̃ provided there exists an open, monotone retraction such that all fibers are pseudo-arcs and any continuum in X̃ joining two different fibers of r intersects X. A continuum is called a continuous pseudo-fan of a compactum X if there are a point and a family ℱ of pseudo-arcs such that , any subcontinuum of intersecting two different elements of ℱ contains c, and ℱ is homeomorphic to X (with...
Contra-continuous functions and strongly -closed spaces.
Coronas of ultrametric spaces
We show that, under CH, the corona of a countable ultrametric space is homeomorphic to . As a corollary, we get the same statements for the Higson’s corona of a proper ultrametric space and the space of ends of a countable locally finite group.