Topological transformation groups and Dugundji compacta

Coset spaces of metrizable groups

“…For the set int(cl(V x)) ∈ γ V , there exists a point y ∈ Y such that y ∈ int(cl(V x)) (since Y is dense in X). Lemma 3 of [22] establishes the inclusion St(y, γ V ) ⊂ int(cl(Oy)). Thus, int(cl(V x)) ⊂ int(cl(Oy)), and hence…”

“…If G is metrizable then the weight of the maximal equiuniformity U on X is countable. In fact, the covers {Ox | x ∈ X}, O ∈ N G (e), constitute a base of the maximal equiuniformity [22]. Since G is metrizable, we can take a countable local base B G (e) at the unity e ∈ G. Then the covers {Ox | x ∈ X}, O ∈ B G (e), constitute a countable base of the maximal equiuniformity on X.…”

“…Since α is a d-open action, for y ∈ Y and O ∈ O, we can choose a set G(O, y) ⊂ O of cardinality w(X) such that G(O, y)y is dense in int(cl(Oy)). By [22,Lemma 4], for any pair O, V ∈ O and x ∈ X, we have…”

Топология Действий И Однородные Пространства

“…Понятие d-открытого или слабо микро-транзитивного действия введено в работе Ф. Анцеля [3]. Оно оказалось достаточно продуктивным в вопросах алгебраической однородности однородного пространства [3], [4], успешно используется при исследовании G-бикомпактификаций [5]- [7], позволяет строить информативную решетку d-открытых отображений на пространстве (свойство Дугунджи) [7], [8].…”

Maximal equivariant compactifications

“…See, for example, R. Brook [8], J. de Vries [50,51,52,53,54,55], Yu.M. Smirnov [41,42,43,44], Antonyan-Smirnov [4], Smirnov-Stoyanov [45], L. Stoyanov [47,48], M. Megrelishvili [24,25,26,27,28,30,31,32], Dikranjan-Prodanov-Stoyanov [10], Megrelishvili-Scarr [34], V. Uspenskij [49], S. Antonyan [2], Gonzalez-Sanchis [14], V. Pestov [37,38], J. van Mill [35], A. Sokolovskaya [46], Google-Megrelishvili [15], Kozlov-Chatyrko [22], N. Antonyan, S. Antonyan and M. Sanchis [3], K. Kozlov [18,19,20,21], N. Antonyan [1], Karasev-Kozlov [17], Ibarlucia-Megrelishvili [16] (and many additional references in these publications).…”