Exponentiability in homotopy slices of TOP and pseudo-slices of CAT.
Exponentiability of perfect maps: Four approaches.
Exponentiable morphisms: Posets, spaces, locales, and Grothendieck toposes.
Exponential domination in function spaces
Given a Tychonoff space and an infinite cardinal , we prove that exponential -domination in is equivalent to exponential -cofinality of . On the other hand, exponential -cofinality of is equivalent to exponential -domination in . We show that every exponentially -cofinal space has a -small diagonal; besides, if is -stable, then . In particular, any compact exponentially -cofinal space has weight not exceeding . We also establish that any exponentially -cofinal space with...
Exponential law for uniformly continous proper maps.
The purpose of this note is to prove the exponential law for uniformly continuous proper maps.
Exponential separability is preserved by some products
We show that exponential separability is an inverse invariant of closed maps with countably compact exponentially separable fibers. This implies that it is preserved by products with a scattered compact factor and in the products of sequential countably compact spaces. We also provide an example of a -compact crowded space in which all countable subspaces are scattered. If is a Lindelöf space and every with is scattered, then is functionally countable; if every with is scattered, then...
Extended Bochner Measurable Selectors.
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 Linear Space-Valued Functions.
Extending maps from dense subspaces .
Extending monotone mappings
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*.
Extension and Selection theorems in Topological spaces with a generalized convexity structure
Extension of bilipschitz maps of compact polyhedra.