A new concept of pre-semicompact L -subsets is introduced, where L is a fuzzy lattice. The pre-semicompact L -subset is semi-precompact, hence it is also semicompact and strongly compact. It is described with collection of pre-semiclosed L -subset, constant α -net and α -level filter base. It is a good L -extension; it is hereditary for pre-semiclosed L -subset; it is finitely additive; it is i...

The aim of this work is the formalization of Chapter 0 Section 4 of [11]. In this paper the definition of meet-continuous lattices is introduced. Theorem 4.2 and Remark 4.3 are proved. Let X, Y be non empty sets, let f be a function from X into Y , and let Z be a non empty subset of X. One can verify that f • Z is non empty. Let us note that every non empty relational structure which is reflexi...

a finite group g is said to be a pos-group if for each x in g the cardinality of the set {y in g | o(y) = o(x)} is a divisor of the order of g. in this paper we study the structure of pos-groups with some cyclic sylow subgroups.

a finite group g is said to be a pos-group if for each x in g the cardinality of the set {y in g | o(y) = o(x)} is a divisor of the order of g. in this paper we study the structure of pos-groups with some cyclic sylow subgroups.

(1) Let L be a non empty reflexive transitive relational structure and x, y be elements of L. If x ≤ y, then compactbelow(x)⊆ compactbelow(y). (2) For every non empty reflexive relational structure L and for every element x of L holds compactbelow(x) is a subset of CompactSublatt(L). (3) For every relational structure L and for every relational substructure S of L holds every subset of S is a s...

A primitive multiple scheme is a Cohen–Macaulay Y such that the associated reduced $$X=Y_{\mathrm{red}}$$ smooth, irreducible, and can be locally embedded in smooth variety of dimension $$\dim (X)+1$$ . If n multiplicity Y, there canonical filtration $$X=X_1\subset X_2\subset \cdots \subset X_n=Y$$ , $$X_i$$ i. The simplest example trivial to line bundle L on X: it nth infinitesimal neighborhoo...

The notation and terminology used here are introduced in the following papers: [18], [13], [17], [14], [19], [7], [1], [8], [6], [20], [3], [9], [2], [10], [15], [16], [5], [11], [4], and [12]. Let us observe that there exists a lattice which is finite. Let us mention that every lattice which is finite is also complete. Let L be a lattice and let D be a subset of the carrier of L. The functor D...

Let $S$ be a finite subset of compact connected Riemann surface $X$ genus $g \geq 2$. $\cat{M}_{lc}(n,d)$ denote the moduli space pairs $(E,D)$, where $E$ is holomorphic vector bundle over and $D$ logarithmic connection on singular $S$, with fixed residues in centre $\mathfrak{gl}(n,\C)$, $n$ $d$ are mutually corpime. $L$ line $D_L$ $S$. $\cat{M}'_{lc}(n,d)$ $\cat{M}_{lc}(n,L)$ spaces parametri...