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.
The article deals with Cantor’s diagonal argument and its alleged philosophical consequences such as that (1) there are more reals than integers and, hence, (2) that some of the reals must be independent of language because the totality of words and sentences is always count-able. My claim is that the main flaw of the argument for the existence of non-nameable (hence unrecognizable) objects or truths lies in a very superficial understanding of what a name or representation actually is., Abstraktní
Článek pojednává o Cantorově diagonálním argumentu a jeho údajných filosofických důsledcích, jako je to, že (1) existuje více reálných než celých čísel, a proto (2) že některé z reals musí být nezávislé na jazyce, protože souhrn slov a vět je vždy počitatelný. Moje tvrzení je, že hlavní chybou argumentu pro existenci nemazatelných (tedy nerozpoznatelných) objektů nebo pravd leží velmi povrchní chápání toho, co vlastně je jméno nebo reprezentace., and Vojtěch Kolman