A -continuum is metrizable if and only if it admits a Whitney map for .
A note on -closed sets and inverse limits.
-directed inverse systems of continuous images of arcs.
Relationships between usual and approximate inverse systems.
Non-metric rim-metrizable continua and unique hyperspace.
Weight and metrizability of inverses under hereditarily irreducible mappings.
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 = {X, p, A} is an inverse system of continuous images of arcs with monotone bonding mappings such that cf (card (A)) ≠ w, then X = lim X is a continuous image of an arc if and only if each proper subsystem {X, p, B} of X with cf(card (B)) = w has the limit which is a continuous image of an arc (Theorem 18).
The Freudenthal space for approximate systems of compacta and some applications.
In this paper we define a space σ() for approximate systems of compact spaces. The construction is due to H. Freudenthal for usual inverse sequences [4, p. 153–156]. We establish the following properties of this space: (1) The space σ() is a paracompact space, (2) Moreover, if is an approximate sequence of compact (metric) spaces, then σ() is a compact (metric) space (Lemma 2.4). We give the following applications of the space σ(): (3) If is an approximate system of continua, then X = lim is a...
Extending generalized Whitney maps
For metrizable continua, there exists the well-known notion of a Whitney map. If is a nonempty, compact, and metric space, then any Whitney map for any closed subset of can be extended to a Whitney map for [3, 16.10 Theorem]. The main purpose of this paper is to prove some generalizations of this theorem.
Relative continuity of the functor
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