The Fundamental Group
نویسندگان
چکیده
This is the next article in a series devoted to the homotopy theory (following [11] and [12]). The concept of fundamental groups of pointed topological spaces has been introduced. Isomorphism of fundamental groups defined with respect to different points belonging to the same component has been stated. Triviality of fundamental group(s) of R n has been shown. the terminology and notation for this paper. We adopt the following convention: p, q, x, y are real numbers and n is a natural number. Next we state a number of propositions: (1) Let G, H be groups and h be a homomorphism from G to H. If h · h −1 = id H and h −1 · h = id G , then h is an isomorphism. (2) For every subset X of I and for every point a of I such that X = ]a, 1] holds X c = [0, a].
منابع مشابه
Fundamental Functor Based on Hypergroups and Groups
The purpose of this paper is to compute of fundamental relations of hypergroups. In this regards first we study some basic properties of fundamental relation of hypergroups, then we show that any given group is isomorphic to the fundamental group of a nontrivial hypergroup. Finally we study the connections between categories of hypergroups and groups via the fundam...
متن کاملDoes Core Stability Training Affect Fundamental Movement Skills in Low Proficiency Children? Evaluation of Performance Process
The present study investigated the effects of 8-weeks of core stability training on fundamental movement skills in children with low proficiency in both locomotor and object control skills. By using a semi-experimental research design. 30 elementary boy students (means age= 8.89 years, SD= 1.06) were recruited and organized in training (n= 15) and control group (n=15). Fundamental movement skil...
متن کاملApplication of fundamental relations on n-ary polygroups
The class of $n$-ary polygroups is a certain subclass of $n$-ary hypergroups, a generalization of D{"o}rnte $n$-arygroups and a generalization of polygroups. The$beta^*$-relation and the $gamma^*$-relation are the smallestequivalence relations on an $n$-ary polygroup $P$ such that$P/beta^*$ and $P/gamma^*$ are an $n$-ary group and acommutative $n$-ary group, respectively. We use the $beta^*$-...
متن کاملOn subgroups of topologized fundamental groups and generalized coverings
In this paper, we are interested in studying subgroups of topologized fundamental groups and their influences on generalized covering maps. More precisely, we find some relationships between generalized covering subgroups and the other famous subgroups of the fundamental group equipped with the compact-open topology and the whisker topology. Moreover, we present some conditions unde...
متن کاملبررسی ویژگیهای آکوستیکی مربوط به کنترل حرکتی گفتار در کودکان لکنتی و غیرلکنتی
Objective Stuttering is a developmental disorder of speech fluency with unknown causes. One of the proposed theories in this field is deficits in speech motor control that is associated with damaged control, timing, and coordination of the speech muscles. Fundamental frequency, fundamental frequency range, intensity, intensity range, and voice onset time are the most important acoustic componen...
متن کاملSome results of semilocally simply connected property
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.
متن کامل