English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $X$ be a (topological) space and let ${\mathscr I}$ be an ideal in $X$,that is, a collection of subsets of $X$ which contains all subsets of itselements and is closed under finite unions. The elements of ${\mathscr I}$ arecalled null. The space $X$ is locally null if each $x$ in $X$ has a nullneighborhood in $X$. Let $C_b(X)$ denote the normed algebra of all continuousbounded real-valued mappings on $X$ equipped with the supremum norm, $C_0(X)$denote the subalgebra of $C_b(X)$ consisting of elements vanishing at infinityand $C_{00}(X)$ the subalgebra of $C_b(X)$ consisting of elements with compactsupport.  We study the normed subalgebra $C^{\mathscr I}_{00}(X)$ of $C_b(X)$consisting of all $f$ in $C_b(X)$ whose support has a null neighborhood in $X$,and the Banach subalgebra $C^{\mathscr I}_0(X)$ of $C_b(X)$ consisting of all$f$ in $C_b(X)$ such that $|f|^{-1}([1/n,\infty))$ has a null neighborhood in$X$ for all positive integer $n$. We prove that if $X$ is a normal locally nullspace then $C^{\mathscr I}_{00}(X)$ and $C^{\mathscr I}_0(X)$ are respectivelyisometrically isomorphic to $C_{00}(Y)$ and $C_0(Y)$ for a unique locallycompact Hausdorff space $Y$; furthermore, $C^{\mathscr I}_{00}(X)$ is dense in$C^{\mathscr I}_0(X)$. We construct $Y$ explicitly as a subspace of theStone--\v{C}ech compactification $\beta X$ of $X$. The space $Y$ is locallycompact (and countably compact, in certain cases), contains $X$ densely, and inspecific cases turns out to be familiar subspaces of $\beta X$. The knowntopological structure of $Y$ enables us to establish several commutativeGelfand--Naimark type theorems and derive results not generally expected to bededucible from the standard Gelfand theory.

Continuous mappings with null support