Dimension and superposition of bounded continuous functions on locally compact, separable metric spaces
نویسندگان
چکیده
منابع مشابه
Uniform Continuity of Continuous Functions on Compact Metric Spaces
A basic theorem asserts that a continuous function on a compact metric space with values in another metric space is uniformly continuous. The usual proofs based on a contradiction argument involving sequences or on the covering property of compact sets are quite sophisticated for students taking a first course on real analysis. We present a direct proof only using results that are established a...
متن کاملON SEQUENCE-COVERING mssc-IMAGES OF LOCALLY SEPARABLE METRIC SPACES
We characterize sequence-covering (resp., 1-sequence-covering, 2-sequence-covering) mssc-images of locally separable metric spaces by means of σ-locally finite cs-networks (resp., sn-networks, so-networks) consisting of א0-spaces (resp., sn-second countable spaces, so-second countable spaces). As the applications, we get characterizations of certain sequence-covering, quotient mssc-images of lo...
متن کاملOn Quotient Π-images of Locally Separable Metric Spaces
We prove that a space is quotient π-image of a locally separable metric space if and only if it has a πand double cs∗cover. We also investigate quotient π-s-images of locally separable metric spaces.
متن کاملOn π-Images of Locally Separable Metric Spaces
To determine what spaces are the images of “nice” spaces under “nice” mappings is one of the central questions of general topology in 1 . In the past, many noteworthy results on images of metric spaces have been obtained. For a survey in this field, see 2 , for example. A characterization for a quotient compact image of a locally separable metric space is obtained in 3 . Also, such a quotient i...
متن کاملCohomological Dimension Theory of Compact Metric Spaces
0. Introduction 1 1. General properties of the cohomological dimension 2 2. Bockstein theory 6 3. Cohomological dimension of Cartesian product 10 4. Dimension type algebra 15 5. Realization theorem 19 6. Test spaces 24 7. Infinite-dimensional compacta of finite cohomological dimension 28 8. Resolution theorems 33 9. Resolutions preserving cohomological dimensions 41 10. Imbedding and approximat...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1993
ISSN: 0166-8641
DOI: 10.1016/0166-8641(93)90056-j