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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We show that all sufficiently nice $\lambda$-sets are countable densehomogeneous ($\mathsf{CDH}$). From this fact we conclude that for everyuncountable cardinal $\kappa \le \mathfrak{b}$ there is a countable densehomogeneous metric space of size $\kappa$. Moreover, the existence of a meagerin itself countable dense homogeneous metric space of size $\kappa$ isequivalent to the existence of a $\lambda$-set of size $\kappa$. On the otherhand, it is consistent with the continuum arbitrarily large that every$\mathsf{CDH}$ metric space has size either $\omega_1$ or size $\mathfrak c$.An example of a Baire $\mathsf{CDH}$ metric space which is not completelymetrizable is presented. Finally, answering a question of Arhangel'skii and vanMill we show that that there is a compact non-metrizable $\mathsf{CDH}$ spacein ZFC.

Countable dense homogeneity and $\lambda$-sets