Countable Fuzzy Topological Space and Countable Fuzzy Topological Vector Space

This paper deals with countable fuzzy topological spaces, a generalization of the notion of fuzzy topological spaces. A collection of fuzzy sets F on a universe X forms a countable fuzzy topology if in the definition of a fuzzy topology, the condition of arbitrary supremum is relaxed to countable supremum. In this generalized fuzzy structure, the continuity of fuzzy functions and some other related properties are studied. Also the class of countable fuzzy topological vector spaces as a generalization of the class of fuzzy topological vector spaces has been introduced and investigated

Weakly fuzzy topological entropy

summary:In 2005, İ. Tok fuzzified the notion of the topological entropy R. A. Adler et al. (1965) using the notion of fuzzy compactness of C. L. Chang (1968). In the present paper, we have proposed a new definition of the fuzzy topological entropy of fuzzy continuous mapping, namely weakly fuzzy topological entropy based on the notion of weak fuzzy compactness due to R. Lowen (1976) along with its several properties. We have shown that the topological entropy R. A. Adler et al. (1965) of continuous mapping $\psi \colon (X,\tau )\rightarrow (X,\tau )$, where $(X,\tau )$ is compact, is equal to the weakly fuzzy topological entropy of $\psi \colon (X,\omega (\tau ))\rightarrow (X,\omega (\tau ))$. We have also established an example that shows that the fuzzy topological entropy of İ. Tok (2005) cannot give such a bridge result to the topological entropy of Adler et al. (1965). Moreover, our definition of the weakly fuzzy topological entropy can be applied to find the topological entropy (namely weakly fuzzy topological entropy $h_w(\psi )$) of the mapping $\psi \colon X\rightarrow X$ (where $X$ is either compact or weakly fuzzy compact), whereas the topological entropy $h_a(\psi )$ of Adler does not exist for the mapping $\psi \colon X\rightarrow X$ (where $X$ is non-compact weakly fuzzy compact). Finally, a product theorem for the weakly fuzzy topological entropy has been established

Conference Program

Document provides a list of the sessions, speakers, workshops, and committees of the 32nd Summer Conference on Topology and Its Applications

Fuzzy Topology, Quantization and Gauge Invariance

Dodson-Zeeman fuzzy topology considered as the possible mathematical framework of quantum geometric formalism. In such formalism the states of massive particle m correspond to elements of fuzzy manifold called fuzzy points. Due to their weak (partial) ordering, m space coordinate x acquires principal uncertainty dx. It's shown that m evolution with minimal number of additional assumptions obeys to schroedinger and dirac formalisms in norelativistic and relativistic cases correspondingly. It's argued that particle's interactions on such fuzzy manifold should be gauge invariant.Comment: 12 pages, Talk given on 'Geometry and Field Theory' conference, Porto, July 2012. To be published in Int. J. Theor. Phys. (2015