The notation and terminology used in this paper have been introduced in the following articles: [20], [9], [25], [7], [8], [4], [16], [24], [21], [19], [13], [18], [23], [1], [2], [10], [5], [17], [11], [3], [22], [14], [12], [6], [26], and [15]. We use the following convention: i, j, n denote natural numbers, f , g, h, k denote finite sequences of elements of R, and M , N denote non empty metr...

Proof. There exists an open neighborhood W of xgcb such that clsWCZ U, where els W denotes the closure of W. Let [ATjfc|fe = l, 2, • • • ] be a neighborhood base at ~1 which is closed. Moreover WEW, i.e. 4>UxEW. Thus there exists k such that ATJItCWCcls W. Hence xECk. Now from WlCU...

In this study, we introduce some well-known definitions and properties for multi-valued functions. We present new such as, m-retraction, m-section, m-homeomorphism, m-HEP reducible function. give a result on the relation between multi-homotopy groups m-homeomorphism. also deal with of m-HEP.