-movable and -calm compacta and their images
A counterexample concerning products in the shape category
We exhibit a metric continuum X and a polyhedron P such that the Cartesian product X × P fails to be the product of X and P in the shape category of topological spaces.
A functional S-dual in a strong shape category
In the S-category (with compact-open strong shape mappings, cf. §1, instead of continuous mappings, and arbitrary finite-dimensional separable metrizable spaces instead of finite polyhedra) there exists according to [1], [2] an S-duality. The S-dual , turns out to be of the same weak homotopy type as an appropriately defined functional dual (Corollary 4.9). Sometimes the functional object is of the same weak homotopy type as the “real” function space (§5).
A strong shape theory with S-duality
A suspension theorem for the proper homotopy and strong shape theories
A Whitehead theorem in CG-shape
Addendum to "Čech and Steenrod homotopy theory with applications to geometric topology"
Algebraic theory of fundamental dimension [Book]
Algebraic topology for proper shape theory
An approach to shape covering maps.
In this note we give an approach to shape covering maps which is comparable to that of *-fibrations (Mardesic and Rushing (1978)). The introduced notion conserves some important properties of usual covering maps.
An extension and axiomatic characterization of Borsuk's theory of shape
An intrinsic characterization of the shape of paracompacta by means of non-continuous single-valued maps.
An introduction to shape theory for the nonspecialist
An R-stable ANR which is not FR-stable
Approximate polyhedra, resolutions of maps and shape fibrations
Approximative expansions of maps into inverse systems
Bemerkungen zur Borel-Moore-Homologie.
Borsuk's quasi-equivalence is not transitive
Borsuk's quasi-equivalence relation on the class of all compacta is considered. The open problem concerning transitivity of this relation is solved in the negative. Namely, three continua X, Y and Z lying in ℝ³ are constructed such that X is quasi-equivalent to Y and Y is quasi-equivalent to Z, while X is not quasi-equivalent to Z.
Categorical strong shape theory
Čech methods and the adjoint functor theorem