Concerning hereditarily locally connected continua
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 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
Connectedness in monotone spaces.
Connectedness in ordered topological spaces
Connections between connected topological spaces on the set of positive integers
In this paper we introduce a connected topology T on the set ℕ of positive integers whose base consists of all arithmetic progressions connected in Golomb’s topology. It turns out that all arithmetic progressions which are connected in the topology T form a basis for Golomb’s topology. Further we examine connectedness of arithmetic progressions in the division topology T′ on ℕ which was defined by Rizza in 1993. Immediate consequences of these studies are results concerning local connectedness of...
Connectivity properties for subspaces of function spaces determined by fixed points.
Connectivity properties in hyperspaces and product spaces
Connectivity properties of sequential Boolean algebras
Connexité locale
Countable locally connected Urysohn spaces
Courbe des trisecantes a une courbe lisse de P3 de degre d > 2g + 1.
C-separated sets and unicoherence
Cut points in abcohesive, aposyndetic, and semi-locally connected spaces.
Cutting description of trivial 1-cohomology
A characterisation of trivial 1-cohomology, in terms of some connectedness condition, is presented for a broad class of metric spaces.