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

In this paper, we analyze the fundamental group $\pi_1(\SigmaX,\overline{x_0})$ of the reduced suspension $\Sigma X$ where $(X,x_0)$ is anarbitrary based Hausdorff space. We show that $\pi_1(\Sigma X,\overline{x_0})$is canonically isomorphic to a direct limit$\varinjlim_{A\in\mathscr{P}}\pi_1(\Sigma A,\overline{x_0})$ where each group$\pi_1(\Sigma A,\overline{x_0})$ is isomorphic to a finitely generated freegroup or the infinite earring group. A direct consequence of thischaracterization is that $\pi_1(\Sigma X,\overline{x_0})$ is locally free forany Hausdorff space $X$. Additionally, we show that $\Sigma X$ is simplyconnected if and only if $X$ is sequentially $0$-connected at $x_0$.

Fundamental groups of reduced suspensions are locally free