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

In this paper we focus on the set-open topologies on the group$\mathcal{H}(X)$ of all self-homeomorphisms of a topological space $X$ whichyield continuity of both the group operations, product and inverse function. Asa consequence, we make the more general case of Dijkstra's theorem. In thiscase a homogeneously encircling family $\mathcal{B}$ consists of regular opensets and the closure of every set from $\mathcal{B}$ is contained in the finiteunion of connected sets from $\mathcal{B}$. Also we proved that the zero-cozerotopology of $\mathcal{H}(X)$ is the relativisation to $\mathcal{H}(X)$ of thecompact-open topology of $\mathcal{H}(\beta X)$ for any Tychonoff space $X$ andevery homogeneous zero-dimensional space $X$ can be represented as the quotientspace of a topological group with respect to a closed subgroup.

On homeomorphism groups and the set-open topology