An extension theorem for separately continuous functions and its application to functional analysis
An extension theorem for sober spaces and the Goldman topology.
An extension to the non-metric case of a theorem of Glasner.
An iff fixed point criterion for continuous self-mappings on a complete metric space. (Summary).
An iff fixed point criterion for continuous self-mappings on a complete metric space.
An implicit-function theorem for a class of monotone generalized equations
An independency result in connectification theory
A space is called connectifiable if it can be densely embedded in a connected Hausdorff space. Let be the following statement: “a perfect -space with no more than clopen subsets is connectifiable if and only if no proper nonempty clopen subset of is feebly compact". In this note we show that neither nor is provable in ZFC.
An index and a Nielsen number for n-valued multifunctions
An infinitary version of Sperner's Lemma
We prove an extension of the well-known combinatorial-topological lemma of E. Sperner to the case of infinite-dimensional cubes. It is obtained as a corollary to an infinitary extension of the Lebesgue Covering Dimension Theorem.
An infinite-dimensional subspace of consisting of functions with no finite one-sided derivatives.
An insertion theorem for real functions
An integral theorem and its applications to coincidence theorems
An interesting class of ideals in subalgebras of containing
In the present paper we give a duality between a special type of ideals of subalgebras of containing and -filters of by generalization of the notion -ideal of . We also use it to establish some intersecting properties of prime ideals lying between and . For instance we may mention that such an ideal becomes prime if and only if it contains a prime ideal. Another interesting one is that for such an ideal the residue class ring is totally ordered if and only if it is prime.
An interesting plane dendroid
An internal characterization of WI spaces
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 invariant for continuous mappings
An invariant of bi-Lipschitz maps
A new numerical invariant for the category of compact metric spaces and Lipschitz maps is introduced. This invariant takes a value less than or equal to 1 for compact metric spaces that are Lipschitz isomorphic to ultrametric ones. Furthermore, a theorem is provided which makes it possible to compute this invariant for a large class of spaces. In particular, by utilizing this invariant, it is shown that neither a fat Cantor set nor the set is Lipschitz isomorphic to an ultrametric space.
An irrational problem
Given a topological space ⟨X,⟩ ∈ M, an elementary submodel of set theory, we define to be X ∩ M with topology generated by . Suppose is homeomorphic to the irrationals; must ? We have partial results. We also answer a question of Gruenhage by showing that if is homeomorphic to the “Long Cantor Set”, then .