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The a-congruences on S(X) and the S-equivalences on X.

H. Pei (1993)

Semigroup forum

The automorphism group of the Lebesgue measure has no non-trivial subgroups of index $< 2^{ω}$

Maciej Malicki (2013)

Colloquium Mathematicae

We show that the automorphism group Aut([0,1],λ) of the Lebesgue measure has no non-trivial subgroups of index $< 2^{ω}$ .

The Baire property in remainders of topological groups and other results

Aleksander V. Arhangel'skii (2009)

Commentationes Mathematicae Universitatis Carolinae

It is established that a remainder of a non-locally compact topological group $G$ has the Baire property if and only if the space $G$ is not Čech-complete. We also show that if $G$ is a non-locally compact topological group of countable tightness, then either $G$ is submetrizable, or $G$ is the Čech-Stone remainder of an arbitrary remainder $Y$ of $G$ . It follows that if $G$ and $H$ are non-submetrizable topological groups of countable tightness such that some remainders of $G$ and $H$ are homeomorphic, then the spaces...

The Banach contraction mapping principle and cohomology

Ludvík Janoš (2000)

Commentationes Mathematicae Universitatis Carolinae

By a dynamical system $(X, T)$ we mean the action of the semigroup $(ℤ^{+}, +)$ on a metrizable topological space $X$ induced by a continuous selfmap $T : X \to X$ . Let $M (X)$ denote the set of all compatible metrics on the space $X$ . Our main objective is to show that a selfmap $T$ of a compact space $X$ is a Banach contraction relative to some $d_{1} \in M (X)$ if and only if there exists some $d_{2} \in M (X)$ which, regarded as a $1$ -cocycle of the system $(X, T) \times (X, T)$ , is a coboundary.

The congruences on S(X) which commute with V.

S. Subbiah, K.D. jr. Magill, W. Barit (1987)

Semigroup forum

The equicontinuous structure relation of a unicoherent point-transitive flow

Mark Wochele (1984)

Fundamenta Mathematicae

The equivariant universality and couniversality of the Cantor cube

Michael G. Megrelishvili, Tzvi Scarr (2001)

Fundamenta Mathematicae

Let ⟨G,X,α⟩ be a G-space, where G is a non-Archimedean (having a local base at the identity consisting of open subgroups) and second countable topological group, and X is a zero-dimensional compact metrizable space. Let $⟨ H ({0, 1}^{ℵ ₀}), {0, 1}^{ℵ ₀}, τ ⟩$ be the natural (evaluation) action of the full group of autohomeomorphisms of the Cantor cube. Then (1) there exists a topological group embedding $φ : G ↪ H ({0, 1}^{ℵ ₀})$ ; (2) there exists an embedding $ψ : X ↪ {0, 1}^{ℵ ₀}$ , equivariant with respect to φ, such that ψ(X) is an equivariant retract of ${0, 1}^{ℵ ₀}$ with respect to φ...

The largest proper congruence on S(X).

Magill, K.D.jun. (1984)

International Journal of Mathematics and Mathematical Sciences

The largest proper regular ideal of $S (X)$

Kenneth D., Jr. Magill (1996)

Czechoslovak Mathematical Journal

The local contractibility of the homeomorphism space of a 2-polyhedron

R. Reese (1972)

Fundamenta Mathematicae

The local weight of an effective locally compact transformation group and the dimension of $L^{2} (G)$

J. de Vries (1978)

Colloquium Mathematicae

The monomorphism semigroup of S(X).

K.D. jr. Magill (1986)

Semigroup forum

The partially ordered collection of regular ...-classes of S(X).

K.D. Jr. Magill, S. Subbiah (1977)

Aequationes mathematicae

The quantum double of a (locally) compact group.

Koornwinder, T.H., Muller, N.M. (1997)

Journal of Lie Theory

The topology of the unit interval is not uniquely determined by its continuous self maps among set systems

Jiří Rosický (1974)

Colloquium Mathematicae

The universal semilattice compactification of a semigroup.

Ebrahimi Vishki, H.R., Pourabdollah, M.A. (1999)

International Journal of Mathematics and Mathematical Sciences

Topological Galois spaces

P. Fletcher, R. Snider (1970)

Fundamenta Mathematicae

Topological semigroups and Kirk's question

Aleksander Całka (1987)

Colloquium Mathematicae

Topologies on the Group of Self Homeomorphisms of the Cantor Set

Michael Sears (1971)

Matematický časopis

Transformation groups with no equicontinuous minimal set

Jason Gait (1972)

Compositio Mathematica

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