# A. A. Rakhimov

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Articles: 3

### Strong base for fuzzy topology

Methods Funct. Anal. Topology 17 (2011), no. 4, 350-355

It is known that a base for a traditional topology, or for a $L$-topology, $\tau$, is a subset ${\mathcal B}$ of $\tau$ with the property that every element $G\in \tau$ can be written as a union of elements of ${\mathcal B}$. In the classical case it is equivalent to say that $G\in \tau$ if and only if for any $x\in G$ we have $B\in {\mathcal B}$ satisfying $x\in B \subseteq G$. This latter property is taken as the foundation for a notion of strong base for a $L$-topology. Characteristic properties of a strong base are given and among other results it is shown that a strong base is a base, but not conversely.

### On mixing and completely mixing properties of positive $L^1$-contractions of finite real W* -algebras

Methods Funct. Anal. Topology 16 (2010), no. 3, 259-263

We consider a non-commutative real analogue of Akcoglu and Sucheston's result about the mixing properties of positive L$^1$-contractions of the L$^1$-space associated with a measure space with probability measure. This result generalizes an analogous result obtained for the L$^1$-space associated with a finite (complex) W$^*$-algebras.

### Actions of finite groups on the hyperfinite real type II$_1$ factor

A. A. Rakhimov

Methods Funct. Anal. Topology 4 (1998), no. 3, 72-83