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.
Gynogenetic diploids were produced from the eggs of natural tetraploid loach Misgurnus anguillicaudatus (Pisces: Cobitidae) without any manipulation for chromosome duplication. When eggs of a four-year-old diploid gynogenetic individual were fertilized with spermatozoa of specimens from normal diploid and natural tetraploid lines, viable diploid and triploid progeny were produced, respectively. Thus, egg nucleus of the diploid gynogen is haploid. In the gonads of diploid progeny, diploid (2n = 50) and tetraploid (4n = 100) mitotic metaphases were observed. The majority of oocytes (76%) showed regular 25 bivalents as in normal diploids, but the other 16% showed a few univalents. The remaining 8% exhibited about 50 bivalents, suggesting chromosome duplication by premeiotic endomitosis. In the testes, a few spermatocytes (6%) showed normal 25 bivalents, but 86% contained various number of univalents and the remaining 8% contained about 50 bivalents. No peaks of spermatozoa were identified in the testis by flow cytometry. In the triploid progeny, triploid (3n = 75) and hexaploid (6n = 150) mitotic metaphases were observed in both ovaries and testes. Most meiotic figures (about 90%) contained approximately 25 bivalents and 25 univalents in both sexes; the rest contained approximately 75 or more bivalents. Spermatozoa were not identified in the testis by flow cytometry. Thus, the diploid males between the diploid gynogens and common diploid, and both sexes of triploids between the diploid gynogens and tetraploid, show aberrant meioses such as frequent formation of univalents, but the diploid females seem to be less affected.