Continua that are approximative absolute neighborhood retracts (AANR’s) are characterized as absolute terminal retracts, i.e., retracts of continua in which they are embedded as terminal subcontinua. This implies that any AANR continuum has a dense arc component, and that any ANR continuum is an absolute terminal retract. It is proved that each absolute retract for any of the classes of: tree-like continua, $\lambda $-dendroids, dendroids, arc-like continua and arc-like $\lambda $-dendroids is an approximative absolute retract (so it is an AANR). Consequently, all these continua have the fixed point property, which is a new result for absolute retracts for tree-like continua. Related questions are asked.
This study deals with a short but little researched episode in the life of Henry of Isernia, an Italian master of ars dictaminis, who came to the court of King Ottokar II of Bohemia in the early 1270s. Henry’s letter collection contains nine letters relating to his temporary stay at the Premonstratensian monastery in Strahov. These letters are impressive, but hardly interpretable, historical sources, and are also the only ones describing the circumstances of the election of a new Abbot of Strahov that probably took place in 1274. The reliability and credibility of Henry’s sometimes exaggerated and emotionally charged narratives were assessed by comparing their historical and biographical content with existing documents and memorial sources, such as monastery necrologies and annals.
Torsion-free covers are considered for objects in the category $q_2.$ Objects in the category $q_2$ are just maps in $R$-Mod. For $R = {\mathbb Z},$ we find necessary and sufficient conditions for the coGalois group $G(A \longrightarrow B),$ associated to a torsion-free cover, to be trivial for an object $A \longrightarrow B$ in $q_2.$ Our results generalize those of E. Enochs and J. Rado for abelian groups.
The inhibitory potential of primary and secondary reproductives was studied using half-orphaned colonies of Kalotermes flavicollis. Both primary and secondary reproductives (neotenics) were equally effective in inhibiting the development of replacement reproductives. Single females totally inhibited the development of female secondary reproductives but did not affect the development of male secondary reproductives. Single males had neither a stimulatory nor inhibitory effect on the development of secondary reproductives. The inhibitory ability of pairs of primary reproductives shortly after dealation and at the stage of incipient colony formation (couple with the first batch of eggs) was also examined. While pairs of freshly dealated reproductives were not able to inhibit the development of neotenics, pairs of primary reproductives that had their first batch of eggs, fully inhibited the development of neotenics.