Uniformly holomorphic continuation in locally convex spaces

We investigate the simultaneous uniformly holomorphic continuation of the uniformly holomorphic functions defined in a domain spread of uniform type, (X, ϑ), over a locally convex Hausdorff space E. We construct the envelope of uniform holomorphy of (X, ϑ) with an analogous method of the results of M. Schottenloher (Portugal. Math. 33 (1974)). Finally, we use this construction to the problem of extending uniformly holomorphic maps f: (X, ϑ) → F, with values in a complete locally convex space to the envelope of uniform holomorphy of X.