5 citations · 13 across the 8 of their papers we have counts for
8 papers
Cantor sets with high-dimensional projections
Olga Frolkina
In 1994, J.Cobb constructed a tame Cantor set in each of whose projections into -planes is one-dimensional. We show that an Antoine's necklace can serve as an exam…
Pairwise disjoint Moebius bands in space
Olga Frolkina
V.V.Grushin and V.P.Palamodov proved in 1962 that it is impossible to place in uncountably many pairwise disjoint polyhedra each homeomorphic to the Moebius band. We generali…
All projections of a typical Cantor set are Cantor sets
Olga Frolkina
In 1994, John Cobb asked: given , does there exist a Cantor set in such that each of its projections into -planes is exactly -dimensional? Such sets we…
Wild high-dimensional Cantor fences in , Part I
Olga Frolkina
Let be the Cantor set. For each we construct an embedding such that , for…
A new simple family of Cantor sets in all of whose projections are one-dimensional
Olga Frolkina
In 1994, J.Cobb described a Cantor set in each of whose projections into 2-planes is one-dimensional. A series of works by other authors developing this field follow…
On a question of B.J. Baker and M. Laidacker concerning disjoint compacta in
Olga Frolkina
We describe wild embeddings of polyhedra into which show that the answer to the question of B.J. Baker--M. Laidacker (1989) concerning uncountable families of pairwi…
Most Cantor sets in are in general position with respect to all projections
Olga Frolkina
We prove the theorem stated in the title. This answers a question of John Cobb (1994). We also consider the case of the Hilbert space .
Minimizing the number of Nielsen preimage classes
Olga Frolkina
We find conditions on topological spaces X, Y and nonempty subset B of Y which guarantee that for each continuous map f from X to Y there exists a map g homotopic to f such that Ni…