F. M. Zakirov

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Articles: 1

Strong base for fuzzy topology

A. A. Rakhimov, F. M. Zakirov

↓ Abstract   |   Article (.pdf)

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.


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