A note on nonfragmentability of Banach spaces.
AC holds iff every compact completely regular topology can be extended to a compact Tychonoff topology
We show that AC is equivalent to the assertion that every compact completely regular topology can be extended to a compact Tychonoff topology.
Algunas propiedades del ejemplo de Tychonoff de un espacio regular que no es completamente regular.
C- and C*-quotients in pointfree topology [Book]
Collectionwise normality and the extension of functions on product spaces
Compactification and compactoidification
Compactifications, and ring epimorphisms.
Compact-like properties in hyperspaces
Continuous extenders for pseudometrics
Continuous extenders in normal and collectionwise normal spaces
Does C* -embedding imply C*-embedding in the realm of products with a non-discrete metric factor?
The above question was raised by Teodor Przymusiński in May, 1983, in an unpublished manuscript of his. Later on, it was recognized by Takao Hoshina as a question that is of fundamental importance in the theory of rectangular normality. The present paper provides a complete affirmative solution. The technique developed for the purpose allows one to answer also another question of Przymusiński's.
Dugundji extenders and retracts on generalized ordered spaces
For a subspace A of a space X, a linear extender φ:C(A) → C(X) is called an -extender (resp. -extender) if φ(f)[X] is included in the convex hull (resp. closed convex hull) of f[A] for each f ∈ C(A). Consider the following conditions (i)-(vii) for a closed subset A of a GO-space X: (i) A is a retract of X; (ii) A is a retract of the union of A and all clopen convex components of X; (iii) there is a continuous -extender φ:C(A × Y) → C(X × Y), with respect to both the compact-open topology and...
Espaces -complètement réguliers
Extending complete continuous pseudometrics
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 of sequentially continuous mappings
Extensions of functions defined on product spaces
Extensions of Lebesgue sets and of real-valued functions
Extensions of Zero-sets and of Real-valued Functions.
Filter characterizations of z-, C*-, and C-embeddings