Expandability and its generalizations
Exponentiable morphisms: Posets, spaces, locales, and Grothendieck toposes.
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...
Extending continuous functions on X x Y to subsets of βX x βY
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*.
Extending the ideal of nowhere dense subsets of rationals to a P-ideal
We show that the ideal of nowhere dense subsets of rationals cannot be extended to an analytic P-ideal, ideal nor maximal P-ideal. We also consider a problem of extendability to a non-meager P-ideals (in particular, to maximal P-ideals).
Extension of multisequences and countably uniradial classes of topologies
It is proved that every non trivial continuous map between the sets of extremal elements of monotone sequential cascades can be continuously extended to some subcascades. This implies a result of Franklin and Rajagopalan that an Arens space cannot be continuously non trivially mapped to an Arens space of higher rank. As an application, it is proved that if for a filter on , the class of -radial topologies contains each sequential topology, then it includes the class of subsequential topologies....
Extension of sequentially continuous mappings
Extension properties of Stone-Čech coronas and proper absolute extensors
We characterize, in terms of X, the extensional dimension of the Stone-Čech corona βX∖X of a locally compact and Lindelöf space X. The non-Lindelöf case is also settled in terms of extending proper maps with values in , where L is a finite complex. Further, for a finite complex L, an uncountable cardinal τ and a -set X in the Tikhonov cube we find a necessary and sufficient condition, in terms of , for X to be in the class AE([L]). We also introduce a concept of a proper absolute extensor and...
Extensions of compact continuous maps into decomposable sets
Extensions of functions defined on product spaces
Extensions of topological and semitopological groups and the product operation
The main results concern commutativity of Hewitt-Nachbin realcompactification or Dieudonné completion with products of topological groups. It is shown that for every topological group that is not Dieudonné complete one can find a Dieudonné complete group such that the Dieudonné completion of is not a topological group containing as a subgroup. Using Korovin’s construction of -dense orbits, we present some examples showing that some results on topological groups are not valid for semitopological...
...-Extensions of Topological Spaces II.
Extensions of unbounded topological spaces
Extremally disconnected resolutions of -spaces
E-Zusammenhängende Räume.
Factorization theorems for extensions of maps