The point of continuity property, neighbourhood assignments and filter convergences

• Autorzy: Ahmed Bouziad
• Języki publikacji: EN

Abstrakty

EN

We show that for some large classes of topological spaces X and any metric space (Z,d), the point of continuity property of any function f: X → (Z,d) is equivalent to the following condition:
(*) For every ε > 0, there is a neighbourhood assignment $(V_x)_{x ∈ X}$ of X such that d(f(x),f(y)) < ε whenever $(x,y) ∈ V_y × V_x$.
We also give various descriptions of the filters ℱ on the integers ℕ for which (*) is satisfied by the ℱ-limit of any sequence of continuous functions from a topological space into a metric space.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 28A20: Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
• 54E20: Stratifiable spaces, cosmic spaces, etc.
• 26A21: Classification of real functions; Baire classification of sets and functions
• 54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
• 54C08: Weak and generalized continuity

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2012
• Tom: 218
• Numer: 3
• Strony: 225-242

Daty

wydano

2012

Twórcy

autor

Ahmed Bouziad

• Département de Mathématiques, Université de Rouen, UMR CNRS 6085, Avenue de l'Université, BP 12, F-76801 Saint-Étienne-du-Rouvray, France

Identyfikatory

DOI

10.4064/fm218-3-2