On bouquets
On category-raising and dimension-raising open mappings with discrete fibers
On certain constructions in finitistic spaces.
On certain homological properties of finite-dimensional compacta. Carriers, minimal carriers and bubbles
On chaotic curves
On character and chain conditions in images of products
A scadic space is a Hausdorff continuous image of a product of compact scattered spaces. We complete a theorem begun by G. Chertanov that will establish that for each scadic space X, χ(X) = w(X). A ξ-adic space is a Hausdorff continuous image of a product of compact ordinal spaces. We introduce an either-or chain condition called Property which we show is satisfied by all ξ-adic spaces. Whereas Property is productive, we show that a weaker (but more natural) Property is not productive. Polyadic...
On character of points in the Higson corona of a metric space
We prove that for an unbounded metric space , the minimal character of a point of the Higson corona of is equal to if has asymptotically isolated balls and to otherwise. This implies that under a metric space of bounded geometry is coarsely equivalent to the Cantor macro-cube if and only if and . This contrasts with a result of Protasov saying that under CH the coronas of any two asymptotically zero-dimensional unbounded metric separable spaces are homeomorphic.
On characterizations of classes of metrizable spaces that have transfinite dimension
On classification of weakly infinite-dimensional compacta
On closed mappings
On compact Hausdorff spaces having finitely many types of open subsets
On compact one-to-one continuous images of the real line
On compact spaces which are locally Cantor bundles
On compactifications with continua as remainders
On composants of Hausdorff continua
On composants of solenoids.
On composants of solenoids
It is proved that any two composants of any two solenoids are homeomorphic.
On composants of the bucket handle
On confluently graph-like compacta
For any class 𝒦 of compacta and any compactum X we say that: (a) X is confluently 𝒦-representable if X is homeomorphic to the inverse limit of an inverse sequence of members of 𝒦 with confluent bonding mappings, and (b) X is confluently 𝒦-like provided that X admits, for every ε >0, a confluent ε-mapping onto a member of 𝒦. The symbol 𝕃ℂ stands for the class of all locally connected compacta. It is proved in this paper that for each compactum X and each family 𝒦 of graphs, X is confluently...
On continua having three types of open subsets