if we consider some special conditions, we can assume fundamental group of a topological space as a new topological space. in this paper, we will present a number of theorems in topological fundamental group related to semilocally simply connected property for a topological space.

following the categorical approach to universal algebra through algebraic theories, proposed by f.~w.~lawvere in his phd thesis, this paper aims at introducing a similar setting for general topology. the cornerstone of the new framework is the notion of emph{categorically-algebraic} (emph{catalg}) emph{topological theory}, whose models induce a category of topological structures. we introduce t...

The main purpose of this paper is to introduce the compatibility of $M$-fuzzifying topologies and $M$-fuzzifying convexities, define an $M$-fuzzifying topological convex space, and give a method to generate an $M$-fuzzifying topological convex space. Some characterizations of $M$-fuzzifying topological convex spaces are presented. Finally, the notion of $M$-fuzzifying weak topologies is obtaine...

The main purpose of this paper is to introduce a concept of$L$-fuzzifying topological groups (here $L$ is a completelydistributive lattice) and discuss some of their basic properties andthe structures. We prove that its corresponding $L$-fuzzifyingneighborhood structure is translation invariant. A characterizationof such topological groups in terms of the corresponding$L$-fuzzifying neighborhoo...

Abstract. A topological group H is called ω -narrow if for every neighbourhood V of it’s identity element there exists a countable set A such that V A = H = AV. A semigroup G is called a generalized group if for any x ∈ G there exists a unique element e(x) ∈ G such that xe(x) = e(x)x = x and for every x ∈ G there exists x − 1 ∈ G such that x − 1x = xx − 1 = e(x). Also le...

Vulnerabilities in ActiveX controls are frequently used by attackers to compromise systems using the Microsoft Internet Explorer web browser. A programming or design flaw in an ActiveX control can allow arbitrary code execution as the result of viewing a specially-crafted web page. In this paper, we examine effective techniques for fuzz testing ActiveX controls, using the Dranzer tool developed...

The paper aims at developing new techniques for uncertainty management in expert systems for two generic class of problems using fuzzy Petri net that represents logical connectivity among a set of imprecise propositions. One class of problems addressed in the paper deals with the computation of fuzzy belief of any proposition from the fuzzy beliefs of a set of independent initiating proposition...

In recent years, fuzz testing has proven itself to be one of the most effective techniques for finding correctness bugs and security vulnerabilities in practice. One particular fuzz testing tool, American Fuzzy Lop or AFL, has become popular thanks to its ease-of-use and bug-finding power. However, AFL remains limited in the depth of program coverage it achieves, in particular because it does n...

Taint-style vulnerabilities comprise a majority of fuzzer discovered program faults. These vulnerabilities usually manifest as memory access violations caused by tainted program input. Although fuzzers have helped uncover a majority of taint-style vulnerabilities in software to date, they are limited by (i) extent of test coverage; and (ii) the availability of fuzzable test cases. Therefore, fu...