On invariants of continuous subgroups of the generalized Poincaré group .
Inductive dimensions modulo simplicial complexes and ANR-compacta
We introduce and investigate inductive dimensions 𝒦 -Ind and ℒ-Ind for classes 𝒦 of finite simplicial complexes and classes ℒ of ANR-compacta (if 𝒦 consists of the 0-sphere only, then the 𝒦 -Ind dimension is identical with the classical large inductive dimension Ind). We compare K-Ind to K-Ind introduced by the author [Mat. Vesnik 61 (2009)]. In particular, for every complex K such that K * K is non-contractible, we construct a compact Hausdorff space X with K-Ind X not equal to K-dim X.
Finite dimensions modulo simplicial complexes and -compacta
Finite dimensions defined by means of -coverings
Subspace and addition theorems for extension and cohomological dimensions. A problem of Kuzminov
Ob Otkrytyh Monotonnyh Otobrazheniyah
The Suslinian number and other cardinal invariants of continua
By the Suslinian number Sln(X) of a continuum X we understand the smallest cardinal number κ such that X contains no disjoint family ℂ of non-degenerate subcontinua of size |ℂ| > κ. For a compact space X, Sln(X) is the smallest Suslinian number of a continuum which contains a homeomorphic copy of X. Our principal result asserts that each compact space X has weight ≤ Sln(X)⁺ and is the limit of an inverse well-ordered spectrum of length ≤ Sln(X)⁺, consisting of compacta with weight ≤ Sln(X) and...
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