A theorem on the weak topology of C(X) for compact scattered X
A theory of absolute proper retracts
A theory of proper shape for locally compact metric spaces
A three-dimensional spheroidal space which is not a sphere
A Tikhonov-type theorem for abstract parabolic differential inclusions in Banach spaces
We consider a class of singularly perturbed systems of semilinear parabolic differential inclusions in infinite dimensional spaces. For such a class we prove a Tikhonov-type theorem for a suitably defined subset of the set of all solutions for ε ≥ 0, where ε is the perturbation parameter. Specifically, assuming the existence of a Lipschitz selector of the involved multivalued maps we can define a nonempty subset of the solution set of the singularly perturbed system. This subset is the set of...
A tiny peculiar Fréchet space
A topological application of flat morasses
We define combinatorial structures which we refer to as flat morasses, and use them to construct a Lindelöf space with points of cardinality , consistent with GCH. The construction reveals, it is hoped, that flat morasses are a tool worth adding to the kit of any user of set theory.
A topological characterization of stationary sets
A topological collapse number for all spaces
A topological dichotomy with applications to complex analysis
Let X be a compact topological space, and let D be a subset of X. Let Y be a Hausdorff topological space. Let f be a continuous map of the closure of D to Y such that f(D) is open. Let E be any connected subset of the complement (to Y) of the image f(∂D) of the boundary ∂D of D. Then f(D) either contains E or is contained in the complement of E. Applications of this dichotomy principle are given, in particular for holomorphic maps, including maximum and minimum modulus principles,...
A topological lattice on the set of multifunctions.
A Topological Notion of Boundedness.
A topological property of beta(N).
A topological representation of polarity lattices.
A topological representation of Post algebras and free Post algebras
A topological space is strongly paracompact if and only if for any monotone increasing open cover of it there exists a star-finite open refinement
We get the following result. A topological space is strongly paracompact if and only if for any monotone increasing open cover of it there exists a star-finite open refinement. We positively answer a question of the strongly paracompact property.
A topological version of a combinatorial theorem of Katětov
A topological version of the Schauder theorem
A topology for automata. II.
A topology generated by eventually different functions