It is shown that a barycentrically soft compactum is necessarily an absolute retract of weight ≤ ω1. Since softness of a map is the mapping version of the property of a space to be an absolute retract, the above mentioned result can be considered as mapping version of the Ditor–Haydon Theorem stating that if P (X) is an absolute retract then the compactum X is of weight ≤ ω1 [2]. All spaces con...

We give a short answer to the question in the title: dendrits. Precisely we show that the C∗-algebra C(X) of all complex-valued continuous functions on a compactum X is projective in the category C of all (not necessarily commutative) unital C∗-algebras if and only if X is an absolute retract of dimension dimX ≤ 1 or, equivalently, that X is a dendrit.

We show that for any sufficiently homogeneous metrizable compactum X there is a Polish group G acting continuously on the space of rational numbersQ such that X is its unique G-compactification. This allows us to answer Problem 995 in the ‘Open Problems in Topology II’ book in the negative: there is a one-dimensional Polish groupG acting transitively onQ forwhich theHilbert cube is its uniqueG-...

A homeomorphism f : X → X of a compactum X with metric d is expansive if there is c > 0 such that if x, y ∈ X and x 6= y, then there is an integer n ∈ Z such that d(fn(x), fn(y)) > c. A homeomorphism f : X → X is continuum-wise expansive if there is c > 0 such that if A is a nondegenerate subcontinuum of X, then there is an integer n ∈ Z such that diam fn(A) > c. Clearly, every expansive homeom...

A total of 112 specimens of yellow peacock bass, Cichla kelberi, were collected in the Três Marias Reservoir, upper São Francisco River, State of Minas Gerais, between 2004 and 2005. Twelve species of parasites were collected: two species of ectoparasites (the monogenetic Gussevia sp. and the copepod Ergasilus sp.); and ten species of endoparasites, including four species of adult endoparasites...

In this note we introduce the concept of a quasi-finite complex. Next, we show that for a given countable and locally finite CW complex L the following conditions are equivalent: L is quasi-finite. There exists a [L]-invertible mapping of a metrizable compactum X with e− dimX ≤ [L] onto the Hilbert cube. Finally, we construct an example of a quasi-finite complex L such that its extension type [...