in this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. some results about existence of maximal m-open setsare given. moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.our results are supported by examples and counterexamples.

We study the algorithmic task of finding a large independent set in sparse Erdős– Rényi random graph with $n$ vertices and average degree $d$. The maximum is known to have size $(2 \log d / d)n$ double limit $n \to \infty$ followed by $d \infty$, but best polynomial-time algorithms can only find an half-optimal $(\log d)n$. show that class low-degree polynomial sets no larger, improving upon re...

It is a consequence of known results^) that any compact light open mapping / of one two-dimensional manifold A into another one B has a definite finite degree k(f), that is, there is an integer k(f) such that for each y£j(A),f~l(y) contains exactly k(f) points provided the points of/_l(y) are counted with multiplicity in an obvious manner. Further, considered as a function on the subset O of co...

We present the first open-set language identification experiments using one-class classification models. We first highlight the shortcomings of traditional feature extractionmethods and propose a hashing-based feature vectorization approach as a solution. Using a dataset of 10 languages from different writing systems, we train a One-Class Support Vector Machine using only a monolingual corpus f...

In this paper, the exact formulae for the generalized degree distance, degree distance and reciprocal degree distance of strong product of a connected and the complete multipartite graph with partite sets of sizes m0, m1, . . . , mr&minus1 are obtained. Using the results obtained here, the formulae for the degree distance and reciprocal degree distance of the closed and open fence graphs are co...

Generating a small size connected dominating set (CDS) for message routing in wireless ad hoc networks is always a challenging problem. In a recent paper, a local pruning algorithm called restricted rule-k has been proposed, and succeeds in generating a small size CDS. In this paper, a statistical analysis on the size of the CDS generated is presented. For a network of N nodes (where N → ∞) tha...

The main goal of this paper is to introduce and study a new class of function via the notions of $e$-$theta$-open sets and $e$-$theta$-closure operator which are defined by Özkoç and Aslım [10] called weakly $eR$-open functions and $e$-$theta$-open functions. Moreover, we investigate not only some of their basic properties but also their relationships with other types of already existing topolo...