Concerning almost realcompactifications
Concerning certain minimal cover refineable spaces
Concerning cut point spaces of order three.
Concerning first countable spaces
Concerning hereditarily locally connected continua
Concerning product of paracompact spaces
Concerning products of proximally fine uniform spaces
Concerning Splittability and Perfect Mappings
Concerning the shapes of n-dimensional spheres
Concerning two covering properties
Condiciones suficientes para la paracompacidad-c. Aplicación a un teorema de metrización.
Conditions under which the least compactification of a regular continuous frame is perfect
We characterize those regular continuous frames for which the least compactification is a perfect compactification. Perfect compactifications are those compactifications of frames for which the right adjoint of the compactification map preserves disjoint binary joins. Essential to our characterization is the construction of the frame analog of the two-point compactification of a locally compact Hausdorff space, and the concept of remainder in a frame compactification. Indeed, one of the characterizations...
Conformal mappings and the Plateau-Douglas problem in Riemannian manifolds.
Connected economically metrizable spaces
A topological space is non-separably connected if it is connected but all of its connected separable subspaces are singletons. We show that each connected sequential topological space X is the image of a non-separably connected complete metric space X under a monotone quotient map. The metric of the space X is economical in the sense that for each infinite subspace A ⊂ X the cardinality of the set does not exceed the density of A, . The construction of the space X determines a functor : Top...
Connected Hausdorff subtopologies
A non-connected, Hausdorff space with a countable network has a connected Hausdorff-subtopology iff the space is not-H-closed. This result answers two questions posed by Tkačenko, Tkachuk, Uspenskij, and Wilson [Comment. Math. Univ. Carolinae 37 (1996), 825–841]. A non-H-closed, Hausdorff space with countable -weight and no connected, Hausdorff subtopology is provided.
Connected LCA groups are sequentially connected
We prove that every connected locally compact Abelian topological group is sequentially connected, i.e., it cannot be the union of two proper disjoint sequentially closed subsets. This fact is then applied to the study of extensions of topological groups. We show, in particular, that if is a connected locally compact Abelian subgroup of a Hausdorff topological group and the quotient space is sequentially connected, then so is .
Connected spaces which are not strongly connected
Connectedness and local connectedness of topological groups and extensions
It is shown that both the free topological group and the free Abelian topological group on a connected locally connected space are locally connected. For the Graev’s modification of the groups and , the corresponding result is more symmetric: the groups and are connected and locally connected if is. However, the free (Abelian) totally bounded group (resp., ) is not locally connected no matter how “good” a space is. The above results imply that every non-trivial continuous homomorphism...
Connectedness and strong semicontinuity
Connectedness in fuzzy topology