A density property of the tori and duality
A dimension raising hereditary shape equivalence
We construct a hereditary shape equivalence that raises transfinite inductive dimension from ω to ω+1. This shows that ind and Ind do not admit a geometric characterisation in the spirit of Alexandroff's Essential Mapping Theorem, answering a question asked by R. Pol.
A dimensional property of Cartesian product
We show that the Cartesian product of three hereditarily infinite-dimensional compact metric spaces is never hereditarily infinite-dimensional. It is quite surprising that the proof of this fact (and this is the only proof known to the author) essentially relies on algebraic topology.
A direct description of uniform completion in locales and a characterization of -groups
A discontinuous function with a connected closed graph
A discrete fixed point theorem of Eilenberg as a particular case of the contraction principle.
A discrete version of the Brunn-Minkowski inequality and its stability
In the first part of the paper, we define an approximated Brunn-Minkowski inequality which generalizes the classical one for metric measure spaces. Our new definition, based only on properties of the distance, allows also us to deal with discrete metric measure spaces. Then we show the stability of our new inequality under convergence of metric measure spaces. This result gives as corollary the stability of the classical Brunn-Minkowski inequality for geodesic spaces. The proof of this stability...
A disjointness theorem involving topological entropy
A double-sequence random iteration process for random fixed points of contractive type random operators.
A Dowker group
A dual of the compression-expansion fixed point theorems.
A factorization lemma and its application to realization of mappings as inverse limits
A factorization theorem and its application to extremally disconnected resolutions
A factorization theorem for the transfinite kernel dimension of metrizable spaces
We prove a factorization theorem for transfinite kernel dimension in the class of metrizable spaces. Our result in conjunction with Pasynkov's technique implies the existence of a universal element in the class of metrizable spaces of given weight and transfinite kernel dimension, a result known from the work of Luxemburg and Olszewski.
A few remarks on blowing-up and connectedness.
A few Remarks on Reduced Ideal-products
A few remarks on the set of finite-to-one maps of the Cantor set
A few topological problems
A first countable supercompact Hausdorff space with a closed nonsupercompact subspace
A fixed point approach to the stability of a functional equation of the spiral of Theodorus.