Two examples of non-separable metrizable spaces
نویسندگان
چکیده
منابع مشابه
Continuity in Separable Metrizable and Lindelöf Spaces
Given a map T : X → X on a set X we examine under what conditions there is a separable metrizable or an hereditarily Lindelöf or a Lindelöf topology on X with respect to which T is a continuous map. For separable metrizable and hereditarily Lindelöf, it turns out that there is a such a topology precisely when the cardinality ofX is no greater than the cardinality of the continuum. We go onto pr...
متن کاملContinuity in Separable Metrizable and Lindelöf Spaces
Given a map T : X → X on a set X we examine under what conditions there is a separable metrizable or an hereditarily Lindelöf or a Lindelöf topology on X with respect to which T is a continuous map. For separable metrizable and hereditarily Lindelöf, it turns out that there is such a topology precisely when the cardinality of X is no greater than c, the cardinality of the continuum. We go on to...
متن کاملSome Examples of Non-Metrizable Spaces Allowing a Simple Type-2 Complexity Theory
Representations of spaces are the key device in Type-2 Theory of Effectivity (TTE) for defining computability on non-countable spaces. Almost-compact representations permit a simple measurement of the time complexity of functions using discrete parameters, namely the desired output precision together with “size” information about the argument, rather than continuous ones. We present some intere...
متن کاملTwo More Perfectly Normal Non-metrizable Manifolds
We show that there is a perfectly normal non-metrizable manifold if there is a Luzin subset of the real line, and that there is a countably compact perfectly normal non-metrizable manifold in any model of set-theory obtained by adding Cohen reals to a model of ZFC +♦.
متن کامل- Metrizable Spaces and Their Applications
In this paper we introduce and study so-called k∗-metrizable spaces forming a new class of generalized metric spaces, and display various applications of such spaces in topological algebra, functional analysis, and measure theory. By definition, a Hausdorff topological space X is k∗-metrizable if X is the image of a metrizable space M under a continuous map f : M → X having a section s : X → M ...
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: Colloquium Mathematicum
سال: 1975
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-33-2-209-211