-directed inverse systems of continuous images of arcs.
A chainable continuum not homeomorphic to an inverse limit on [0, 1] with only one bonding map
A factorization lemma and its application to realization of mappings as inverse limits
A note on inverse limits of continuous images of arcs.
The main purpose of this paper is to prove some theorems concerning inverse systems and limits of continuous images of arcs. In particular, we shall prove that if X = {Xa, pab, A} is an inverse system of continuous images of arcs with monotone bonding mappings such that cf (card (A)) ≠ w1, then X = lim X is a continuous image of an arc if and only if each proper subsystem {Xa, pab, B} of X with cf(card (B)) = w1 has the limit which is a continuous image of an arc (Theorem 18).
A note on the non-emptiness of the limit of approximate systems
Short proofs of the fact that the limit space of a non-gauged approximate system of non-empty compact uniform spaces is non-empty and of two related results are given.
A note on -closed sets and inverse limits.
A spectral characterization of skeletal maps
We prove that a map between two realcompact spaces is skeletal if and only if it is homeomorphic to the limit map of a skeletal morphism between ω-spectra with surjective limit projections.
A sum theorem for A-weakly infinite-dimensional spaces
A theorem on expansions into inverse systems of metric spaces
An example in the theory of approximate systems
An approximate inverse sequence of plane continua is constructed which negatively answers a question of S. Mardeši’c related to approximate and usual inverse systems. The example also shows that an important result of M.G. Charalambous cannot be improved. As an application, it is shown that a procedure of making an approximate inverse sequence commutative (“taming”) is discontinuous.
An extension theorem for sober spaces and the Goldman topology.
Approximate inverse systems of uniform spaces and an application of inverse systems
The fundamental properties of approximate inverse systems of uniform spaces are established. The limit space of an approximate inverse sequence of complete metric spaces is the limit of an inverse sequence of some of these spaces. This has an application to the dimension of the limit space of an approximate inverse system. A topologically complete space with is the limit of an approximate inverse system of metric polyhedra of . A completely metrizable separable space with is the limit of an...
Approximate polyhedra, resolutions of maps and shape fibrations
Approximative expansions of maps into inverse systems
Borsuk's Theory of Shape and Cech Homotopy.
Čech homology for movable compacta
Characterizing realcompact spaces as limits of approximate polyhedral systems
Realcompact spaces can be characterized as limits of approximate inverse systems of Polish polyhedra.
Classes of commutative rings characterized by going-up and going-down behavior
Classifying finite-sheeted covering mappings of paracompact spaces.
The main result of the present paper is a classification theorem for finite-sheeted covering mappings over connected paracompact spaces. This theorem is a generalization of the classical classification theorem for covering mappings over a connected locally pathwise connected semi-locally 1-connected space in the finite-sheeted case. To achieve the result we use the classification theorem for overlay structures which was recently proved by S. Mardesic and V. Matijevic (Theorems 1 and 4 of [5]).
Coherent and strong expansions of spaces coincide
In the existing literature there are several constructions of the strong shape category of topological spaces. In the one due to Yu. T. Lisitsa and S. Mardešić [LM1-3] an essential role is played by coherent polyhedral (ANR) expansions of spaces. Such expansions always exist, because every space admits a polyhedral resolution, resolutions are strong expansions and strong expansions are always coherent. The purpose of this paper is to prove that conversely, every coherent polyhedral (ANR) expansion...