Alcuni risultati su proprietà di ricoprimento e sulla spezzabilità
Algebraic characterization of finite (branched) coverings
Every continuous map X → S defines, by composition, a homomorphism between the corresponding algebras of real-valued continuous functions C(S) → C(X). This paper deals with algebraic properties of the homomorphism C(S) → C(X) in relation to topological properties of the map X → S. The main result of the paper states that a continuous map X → S between topological manifolds is a finite (branched) covering, i.e., an open and closed map whose fibres are finite, if and only if the induced homomorphism...
Algebras of functions on mappings.
Almost contra-precontinuous functions.
Almost -closed functions and separation axioms
We introduce a new class of functions called almost -closed and use the functions to improve several preservation theorems of normality and regularity and also their generalizations. The main result of the paper is that normality and weak normality are preserved under almost -closed continuous surjections.
Almost -precontinuous multifunctions.
Almost-Homeomorphisms And Almost-Topological Properties.
An algebraic and logical approach to continuous images
An atomic map onto an arbitrary metric continuum
An Exactly Two-to-One Map from an Indecomposable Chainable Continuum
It is shown that a certain indecomposable chainable continuum is the domain of an exactly two-to-one continuous map. This answers a question of Jo W. Heath.
An example for mappings related to confluence
Confluence of a mapping between topological spaces can be defined by several ways. J.J. Charatonik asked if two definitions of the confluence using the components and quasi-components are equivalent for surjective mappings with compact point inverses. We give the negative answer to this question in Example 2.1.
An example for mappings related to semi-confluence.
An example of a space whose all continuous mappings are almost injective
We show that all continuous maps of a space onto second countable spaces are pseudo-open if and only if every discrete family of nonempty -subsets of is finite. We also prove under CH that there exists a dense subspace of the real line , such that every continuous map of is almost injective and cannot be represented as , where is compact and is countable. This partially answers a question of V.V. Tkachuk in [Tk]. We show that for a compact , all continuous maps of onto second...
An open-perfect mapping on a hereditarily disconnected space onto a connected space
Another note on Levine's decomposition of continuity.
...-Applications dans une variété
Around a quotient space of Bennett-Lutzer's space.
A-spaces and countably bi-quotient maps [Book]
Automorphism groups of complements of points
Bad Wadge-like reducibilities on the Baire space
We consider various collections of functions from the Baire space into itself naturally arising in (effective) descriptive set theory and general topology, including computable (equivalently, recursive) functions, contraction mappings, and functions which are nonexpansive or Lipschitz with respect to suitable complete ultrametrics on (compatible with its standard topology). We analyze the degree-structures induced by such sets of functions when used as reducibility notions between subsets of...