Traditionally, a grammar defining the syntax of programming language is typically both context free and unambiguous. However, recent work suggests that an attractive alternative to use ambiguous grammars,thus postponing task resolving ambiguity end user. If all programs accepted by can be rewritten unambiguously, then parser for said resolvably ambiguous. Guaranteeing resolvable statically---fo...

A space X is said to be κ-resolvable (resp. almost κ-resolvable) if it contains κ dense sets that are pairwise disjoint (resp. almost disjoint over the ideal of nowhere dense subsets). X is maximally resolvable iff it is ∆(X)-resolvable, where ∆(X) = min{|G| : G 6= ∅ open}. We show that every crowded monotonically normal (in short: MN) space is ω-resolvable and almost μ-resolvable, where μ = mi...

in this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  we relate the cohomology of a normal subgroup $n$ of a topological group $g$ and the quotient $g/n$ to the cohomology of $g$. we get the inflation-restriction exact sequence. also, we obtain a seven-term exact cohomology sequence up to dimension 2. we give an interpretation of the first non-a...

We investigate the spectrum for frames with block size four, and discuss several applications to the construction of other combinatorial designs. Our main result is that a frame of type hu, having blocks of size four, exists if and only if u ≥ 5, h ≡ 0 mod 3 and h(u − 1) ≡ 0 mod 4, except possibly where (i) h = 9 and u ∈ {13, 17, 29, 33, 93, 113, 133, 153, 173, 193}; (ii) h ≡ 0 mod 12 and u ∈ {...

In this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  We relate the cohomology of a normal subgroup $N$ of a topological group $G$ and the quotient $G/N$ to the cohomology of $G$. We get the inflation-restriction exact sequence. Also, we obtain a seven-term exact cohomology sequence up to dimension 2. We give an interpretation of the first non-a...

in this paper, some fundamental concepts are given relating to fuzzytopological spaces. then it is shown that there is a contravariant functorfrom the category of the pointed fuzzy topological spaces to the category ofgroups and homomorphisms. also the fuzzy topological spaces which are hopfspaces are investigated and it is shown that a pointed fuzzy toplogicalspace having the same homotopy typ...