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

For a metrizable space $X$ of density $\kappa$, let $PM(X)$ be the space ofcontinuous bounded pseudometrics on $X$ endowed with the uniform convergencetopology. In this paper, its topology shall be classified as follows: (i) If$X$ is finite, then $PM(X)$ is homeomorphic to $\{0\}$ when $X$ is a singleton,and then $PM(X)$ is homeomorphic to $[0,1]^{\kappa(\kappa - 1)/2 - 1} \times[0,1)$ when $\kappa > 1$; (ii) If $X$ is infinite and generalized compact, then$PM(X)$ is homeomorphic to the Hilbert space $\ell_2(2^{< \kappa})$ of density$2^{< \kappa}$; (iii) If $X$ is not generalized compact, then $PM(X)$ ishomeomorphic to the Hilbert space $\ell_2(2^\kappa)$ of density $2^\kappa$.Furthermore, letting $M(X)$ and $AM(X)$ be the spaces of continuous boundedmetrics and bounded admissible metrics on $X$ with the subspace topology of$PM(X)$ respectively, we will recognize their topological types as follows:(iv) If $X$ is infinite and compact, then $M(X) (= AM(X))$ is homeomorphic tothe separable Hilbert space $\ell_2$; (v) In the case that $X$ is not compact,$M(X)$ is homeomorphic to the Hilbert space $\ell_2(2^{\aleph_0})$ if $X$ is$\sigma$-compact, and moreover $AM(X)$ is also homeomorphic to the Hilbertspace $\ell_2(2^{\aleph_0})$ if $X$ is separable locally compact.

The topological classification of spaces of metrics with the uniform convergence topology