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Throughout his paper, the author uses "orientable manifold'' to mean a compact connected orientable 3-manifold without boundary. Such a manifold is known to be a ramified covering over a link of the 3-sphere, in which the ramification index of each singular point is ≤2. If the covering has n leaves, suppose that there are m points of index 2 and 2m points of index 1; such a covering is of type (m,n−2m). The author's main theorem states: Every orientable manifold is a ramified covering of type (1,n−2). He also uses the notion of a "link with a colouring of type (m,n−2m)''; these are intimately related to ramified coverings of type (m,n−2m). He conjectures that every link having a colouring of type (1,n−2) is "separable'', a term too complicated to define here. With this conjecture and his main theorem, he enunciates two further theorems and a second conjecture to show that his two conjectures, if true, would imply the Poincaré hypothesis for 3-manifolds. The author adds a note in proof to say that his first conjecture is false, as will be shown in a forthcoming paper by R. H. Fox. It therefore seems unnecessary to detail the conjectures in this review., Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, TRUE, pub

Let B(H) be the algebra of all bounded linear operators acting on the real separable Hilbert space H and let S={an}∞n=1 be a sequence in H. Consider the linear manifolds CS={AB(H):∑∞n=1||Aan||<∞}and DS={AB(H):{Aan}∞n=1 is summable} of B(H), and MS={xH:∑∞ n=1|(an,x)|<∞} of H. The author proves that CS is not closed, in general, and characterizes the cases when CS is closed in terms of the domain of weak summability of S. If dimMS is finite, or dim(linear spanS) is finite, then CS=DS, but the converse is false., Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, TRUE, pub

Fac. de Ciencias Matemáticas, TRUE, pub

Crónica: Real Academia de Ciencias Exactas, Físicas y Naturales. Fundación del Conde de Cartagena. Cátedra de Matemática (curso de topología)., Fac. de Ciencias Matemáticas, TRUE, pub

Crónica. Real Academia de Ciencias Exactas, Físicas y Naturales. Fundación del Conde de Cartagena. Cátedra de Matemática (curso de topología). Conferencias del Prof. T. R. Bachiller., Fac. de Ciencias Matemáticas, TRUE, pub

Weak sequential convergence defines a topology by the requirement that a set O is open if xn⇀x and x∈O implies almost every xn∈O. This topology, Tc, is considered for a real Hilbert (separable) space. A form for the neighborhoods of the origin is given and Tc is compared with the weak topology. Tc is the finest topology that induces the same topology in bounded sets as the weak topology. Tc is an S-topology for S the set of pre-compact sets. The relation with other S-topologies is also given, Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, TRUE, pub