2 Open and Closed Classes in Cantor Space 5 2.1 Open Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Closed Classes . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 The Compactness Theorem . . . . . . . . . . . . . . . . . . . 7 2.4 Notation For Trees . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 Effective Compactness Theorem . . . . . . . . . . . . . . . . . 8

in this paper, our purpose is twofold. firstly, the tensor andresiduum operations on $l-$nested systems are introduced under thecondition of complete residuated lattice. then we show that$l-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. thus the new representation theorem of$l-$subsets on complete re...

‎in this article we introduce $mu$-filtered fuzzy module with a family of fuzzy submodules.  it shows the relation between $mu$-filtered fuzzy modules and crisp filtered modules by level sets. we investigate fuzzy topology on the $mu$-filtered fuzzy module and apply that to introduce fuzzy completion. finally we extend krull's intersection theorem of fuzzy ideals by using concept $mu$-adic...

Bing-Whitehead Cantor sets were introduced by DeGryse and Osborne in dimension three and greater to produce examples of Cantor sets that were non standard (wild), but still had simply connected complement. In contrast to an earlier example of Kirkor, the construction techniques could be generalized to dimensions bigger than three. These Cantor sets in S are constructed by using Bing or Whitehea...

A Cantor set is a non-empty, compact set that has neither interior nor isolated points. In this paper a Cantor set K ⊆ R is constructed such that every set definable in (R, <,+, ·,K) is Borel. In addition, we prove quantifierelimination and completeness results for (R, <,+, ·,K), making the set K the first example of a modeltheoretically tame Cantor set. This answers questions raised by Friedma...

We determine the constructive dimension of points in random translates of the Cantor set. The Cantor set “cancels randomness” in the sense that some of its members, when added to Martin-Löf random reals, identify a point with lower constructive dimension than the random itself. In particular, we find the Hausdorff dimension of the set of points in a Cantor set translate with a given constructiv...