In this paper, we introduce the notion of weakly e-continuous functions in topological spaces. Weak s-contlnulty and subweak continuity due to Rose [i] are independent of each other and are implied by weak continuity due to Levlne [2]. It is shown that weakly e-continuous surjections preserve connected spaces and that weakly e-contlnuous functions into regular spaces are continuous. Corollary i...

We construct a Lipschitz-free space that is locally almost square but not weakly square; this the first example of such Banach space. also prove result, which indicates geodesic metric spaces are potential characterization for spaces. Lastly, we can have symmetric strong diameter 2 property.

Let e(Tn) be the primitive exponent of a primitive tournament Tn of order n. In this paper, we obtain the following results. 1. Let Tn be a regular or almost regular tournament of order n ≥ 7; then e(Tn) = 3. 2. Let k ∈ {n, n + 1, n + 2}. We give the sufficient and necessary conditions for Tn such that e(Tn) = k, and obtain all Tn’s such that e(Tn) = k.