Exponentially Complete Spaces III
Exponentially complete spaces III.
Exponentially Complete Spaces IV
Exponentially complete spaces IV.
Extended Bochner Measurable Selectors.
Extended contraction principle.
Extended topology: continuity - I
Extended topology: perfect sets
Extended Topology: Structure of Isotonic Functions.
Extenders for vector-valued functions
Given a subset A of a topological space X, a locally convex space Y, and a family ℂ of subsets of Y we study the problem of the existence of a linear ℂ-extender , which is a linear operator extending bounded continuous functions f: A → C ⊂ Y, C ∈ ℂ, to bounded continuous functions f̅ = u(f): X → C ⊂ Y. Two necessary conditions for the existence of such an extender are found in terms of a topological game, which is a modification of the classical strong Choquet game. The results obtained allow us...
Extending complete continuous pseudometrics
Extending continuous functions on X x Y to subsets of βX x βY
Extending Continuous Functions on Zero-Dimensional Spaces.
Extending generalized Whitney maps
For metrizable continua, there exists the well-known notion of a Whitney map. If is a nonempty, compact, and metric space, then any Whitney map for any closed subset of can be extended to a Whitney map for [3, 16.10 Theorem]. The main purpose of this paper is to prove some generalizations of this theorem.
Extending Linear Space-Valued Functions.
Extending maps from dense subspaces .
Extending metrics uniformly
Extending monotone mappings
Extending point-finite covers
Extending real-valued functions in βκ
An Open Coloring Axiom type principle is formulated for uncountable cardinals and is shown to be a consequence of the Proper Forcing Axiom. Several applications are found. We also study dense C*-embedded subspaces of ω*, showing that there can be such sets of cardinality and that it is consistent that ω*{pis C*-embedded for some but not all p ∈ ω*.