A hereditarily indecomposable, hereditarily non-chainable planar tree-like continuum
A hereditarily indecomposable non-metric Hausdorff continuum
A hereditarily infinite dimensional space
A hereditarily normal strongly zero-dimensional space containing subspaces of arbitrarily large dimension
A hereditarily normal strongly zero-dimensional space containing subspaces of arbitrary large dimension
A hereditarily normal strongly zero-dimensional space with a subspace of positive dimension and an N-compact space of positive dimension
A hereditary property of HM-spaces.
A Hilbert cube compactification of the function space with the compact-open topology
Let X be an infinite, locally connected, locally compact separable metrizable space. The space C(X) of real-valued continuous functions defined on X with the compact-open topology is a separable Fréchet space, so it is homeomorphic to the psuedo-interior s = (−1, 1)ℕ of the Hilbert cube Q = [−1, 1]ℕ. In this paper, generalizing the Sakai-Uehara’s result to the non-compact case, we construct a natural compactification (X) of C(X) such that the pair ( (X), C(X)) is homeomorphic to (Q, s). In case...
A hit-and-miss topology for , Cₙ(X) and Fₙ(X)
A hit-and-miss topology () is defined for the hyperspaces , Cₙ(X) and Fₙ(X) of a continuum X. We study the relationship between and the Vietoris topology and we find conditions on X for which these topologies are equivalent.
A homogeneous space of point-countable but not of countable type
We construct an example of a homogeneous space which is of point-countable but not of countable type. This shows that a result of Pasynkov cannot be generalized from topological groups to homogeneous spaces.
A homological selection theorem implying a division theorem for Q-manifolds
We prove that a space M with Disjoint Disk Property is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. This implies that the product M × I² of a space M with the disk is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. The proof of these theorems exploits the homological characterization of Q-manifolds due to Daverman and Walsh, combined with the existence of G-stable points in C-spaces. To establish the existence of such points we prove (and afterward...
A Kirk type characterization of completeness for partial metric spaces.
À la mémoire de Eduard Čech
A lambda-graph system for the Dyck shift and its -groups.
A large -discrete Fréchet space having the Souslin property
A lattice of conditions on topological spaces II
A Lefschetz-type coincidence theorem
A Lefschetz-type coincidence theorem for two maps f,g: X → Y from an arbitrary topological space to a manifold is given: , that is, the coincidence index is equal to the Lefschetz number. It follows that if then there is an x ∈ X such that f(x) = g(x). In particular, the theorem contains well-known coincidence results for (i) X,Y manifolds, f boundary-preserving, and (ii) Y Euclidean, f with acyclic fibres. It also implies certain fixed point results for multivalued maps with “point-like” (acyclic)...
A Lefschetz-type fixed point theorem
A lemma on finite-dimensional covers
A Leray--Schauder alternative for weakly-strongly sequentially continuous weakly compact maps.