Connected CM-homomorphisms into
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...
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 monotone spaces.
Connectedness of some rings of quotients of with the -topology
In this article we define the -topology on some rings of quotients of . Using this, we equip the classical ring of quotients of with the -topology and we show that with the -topology is in fact a subspace of with the -topology. Characterization of the components of rings of quotients of is given and using this, it turns out that with the -topology is connected if and only if is a pseudocompact almost -space, if and only if with -topology is connected. We also observe that...
Connection matrix pairs
We discuss the ideas of Morse decompositions and index filtrations for isolated invariant sets for both single-valued and multi-valued maps. We introduce the definition of connection matrix pairs and present the theorem of their existence. Connection matrix pair theory for multi-valued maps is used to show that connection matrix pairs obey the continuation property. We conclude by addressing applications to numerical analysis. This paper is primarily an overview of the papers [R1] and [R2].
Connectivity functions and retracts
Connectivity functions defined on
Connectivity of diagonal products of Baire one functions
We characterize those Baire one functions f for which the diagonal product x → (f(x), g(x)) has a connected graph whenever g is approximately continuous or is a derivative.
Connectivity properties for subspaces of function spaces determined by fixed points.
Consonance and Cantor set-selectors
It is shown that every metrizable consonant space is a Cantor set-selector. Some applications are derived from this fact, also the relationship is discussed in the framework of hyperspaces and Prohorov spaces.
Constant and variable drop theorems on metrizable locally convex spaces
Constant selections and minimax inequalities
In this paper, we establish two constant selection theorems for a map whose dual is upper or lower semicontinuous. As applications, matching theorems, analytic alternatives, and minimax inequalities are obtained.
Constructing Banaschewski compactification without Dedekind completeness axiom.
Constructing exotic retracts, factors of manifolds, and generalized manifolds via decompositions
Containing spaces for planar rational compacta [Book]
Continua whose local homeomorphisms are homeomorphisms
Continua with the periodic-recurrent property.
Continuity Based on Convergence and Lower Complete Distributive Lattices instead of Directed Sets