33 citations · 154 across the 37 of their papers we have counts for
4 papers · 2 filters
Lim colim versus colim lim. I
Sergey A. Melikhov
We study a model situation in which direct limit () and inverse limit () do not commute, and offer some computations of their "commutator". The homology of a se…
Lim colim versus colim lim. II: Derived limits over a pospace
Sergey A. Melikhov
Čech cohomology of a separable metrizable space is defined in terms of cohomology of its nerves (or ANR neighborhoods) whereas Steenrod-Sitnikov homology $H_n(X)…
Algebraic topology of Polish spaces. II: Axiomatic homology
Sergey A. Melikhov
Milnor proved two uniqueness theorems for axiomatic (co)homology: one for pairs of compacta (1960) and another, in particular, for pairs of countable simplicial complexes (1961). W…
Fine shape I
Sergey A. Melikhov
We introduce and develop fine shape, which has a very simple definition and aims to supersede all previously known shape theories for metrizable spaces. The problem with known shap…