Topology of Limit Spaces of Uncountable Inverse Spectra

Abstract

An f/IO rotating mirror smear camera capable of sweep speeds up to I mmpec-' is described. The simple construction of the camera does not involve either optical polishing of the mirror surface or dynamic balancing of the rotating mirror assembly.

A Surjective Characterization of Dugundji Spaces

“…A major breakthrough in the characterization of Dugundji spaces and Milutin spaces was achieved by R. Haydon [4] showing that every Dugundji space is a Milutin space and that the notions of Dugundji space and absolute extensor for compact zero-dimensional spaces (AE(O-dim)) are equivalent. Recently in his paper [7] Shchepin gave another characterization of the class of Dugundji spaces and produced an example of a zero-dimensional space of weight w2 that is a non-Dugundji Milutin space.In this paper we shall consider continuous surjections satisfying the zero-dimensional lifting property (z.d.l.p.) which will lead to a new characterization of Dugundji spaces.…”

“…-> F. By Lemma 2 the set-valued function that takes each r G R into the support of the probability measure 8^r) ° u satisfies the hypotheses of Lemma 1 and so it admits a continuous selection 0: R-^> S. In particular, 0(r) is an element of the fibre ^~x(<p(r)) for all r E R, i.e., <f> = «f/ ° 0. □ In order to infer that the restriction to metrizability in the preceding proposition is indeed essential we follow Shchepin's terminology and denote by expn(S) the space of all nonempty subsets of S of cardinality < « furnished with the finite topology (see [7] for more details). In passing we mention that the space exp2(D"2) was exhibited in [7] as the first known example of a Milutin space that is not a Dugundji space.…”

“…□ In order to infer that the restriction to metrizability in the preceding proposition is indeed essential we follow Shchepin's terminology and denote by expn(S) the space of all nonempty subsets of S of cardinality < « furnished with the finite topology (see [7] for more details). In passing we mention that the space exp2(D"2) was exhibited in [7] as the first known example of a Milutin space that is not a Dugundji space. The fact that for any set A the space exp2(LV*) is a Milutin space is an easy consequence of the following observation.…”

Econographication

“…It is based on the uses of the topological dimension of a compact metric space based on the concept of cuts [23]. The third definition about dimension is given by Urysohn and Menger [24], they defined dimension as "between any compactum and a point not belonging to it". These four authors are sharing common concepts into its definitions about dimension such as the uses of spaces, subspaces, sets, subsets, partitioned and cut concepts.…”

On the absolutes of compact spaces with a minimally acting group

“…We refer to Haydon [8] or Scepin [11] for basic material on Dugundji spaces. Shapiro [13] proved the following fact:…”