The Topological Entropy of the Transformation x ... ax (1-x).
The topological proof of the Nachbin-Shirota's theorem
The topology of the Banach–Mazur compactum
Let J(n) be the hyperspace of all centrally symmetric compact convex bodies , n ≥ 2, for which the ordinary Euclidean unit ball is the ellipsoid of maximal volume contained in A (the John ellipsoid). Let be the complement of the unique O(n)-fixed point in J(n). We prove that: (1) the Banach-Mazur compactum BM(n) is homeomorphic to the orbit space J(n)/O(n) of the natural action of the orthogonal group O(n) on J(n); (2) J(n) is an O(n)-AR; (3) is an Eilenberg-MacLane space ; (4) is noncontractible;...
The volume near the zeroes of a smooth function.
The Whitehead and the Smale theorems in shape theory [Book]
The -property in
The -property of a Riesz space (real vector lattice) is: For each sequence of positive elements of , there is a sequence of positive reals, and , with for each . This condition is involved in studies in Riesz spaces of abstract Egoroff-type theorems, and of the countable lifting property. Here, we examine when “” obtains for a Riesz space of continuous real-valued functions . A basic result is: For discrete , has iff the cardinal , Rothberger’s bounding number. Consequences and...
Théorème d'Ascoli et application aux groupes topologiques localement compacts en analyse non standard
Theorems fo Stone-Weierstrass Type for Non-Compact Spaces.
Theorems on multifunctions satisfying a rational inequality
There is no universal separable Fréchet or sequential compact space
There is no universal totally disconnected space
Three countable connected spaces
Three technical tools in uniform spaces
Three variants of a Kuratowski's theorem
Tibor Neubrunn (1929 – 1990) [Book]
Tietze's extension theorem.
Tightness and resolvability
We prove resolvability and maximal resolvability of topological spaces having countable tightness with some additional properties. For this purpose, we introduce some new versions of countable tightness. We also construct a couple of examples of irresolvable spaces.
Tightness and π-character in centered spaces
We continue an investigation into centered spaces, a generalization of dyadic spaces. The presence of large Cantor cubes in centered spaces is deduced from tightness considerations. It follows that for centered spaces X, πχ(X) = t(X), and if X has uncountable tightness, then t(X) = supκ : ⊂ X. The relationships between 9 popular cardinal functions for the class of centered spaces are justified. An example is constructed which shows, unlike the dyadic and polyadic properties, that the centered...
Tightness of compact spaces is preserved by the -equivalence relation
We prove that if there is an open mapping from a subspace of onto , then is a countable union of images of closed subspaces of finite powers of under finite-valued upper semicontinuous mappings. This allows, in particular, to prove that if and are -equivalent compact spaces, then and have the same tightness, and that, assuming , if and are -equivalent compact spaces and is sequential, then is sequential.