The continuity of the inversion and the structure of maximal subgroups in countably compact topological semigroups

In this paper we search for conditions on a countably compact (pseudo-compact) topological semigroup under which: (i) each maximal subgroup $H(e)$ in $S$ is a (closed) topological subgroup in $S$; (ii) the Clifford part $H(S)$(i.e. the union of all maximal subgroups) of the semigroup $S$ is a closed subset in $S$; (iii) the inversion $\operatorname{inv}\colon H(S)\to H(S)$ is continuous; and (iv) the projection $\pi\colon H(S)\to E(S)$, $\pi\colon x\longmapsto xx^{-1}$, onto the subset of idempotents $E(S)$ of $S$, is continuous

Carbon dioxide fluxes increase from day to night across European streams

Globally, inland waters emit over 2 Pg of carbon per year as carbon dioxide, of which the majority originates from streams and rivers. Despite the global significance of fluvial carbon dioxide emissions, little is known about their diel dynamics. Here we present a large-scale assessment of day- and night-time carbon dioxide fluxes at the water-air interface across 34 European streams. We directly measured fluxes four times between October 2016 and July 2017 using drifting chambers. Median fluxes are 1.4 and 2.1 mmol m−2 h−1 at midday and midnight, respectively, with night fluxes exceeding those during the day by 39%. We attribute diel carbon dioxide flux variability mainly to changes in the water partial pressure of carbon dioxide. However, no consistent drivers could be identified across sites. Our findings highlight widespread day-night changes in fluvial carbon dioxide fluxes and suggest that the time of day greatly influences measured carbon dioxide fluxes across European streams