منابع مشابه
Linearly Ordered Topological Spaces
This work is devoted to the study of certain cardinality modifications of paracompactness and compactness in the setting of linearly ordered spaces. Some of the concepts treated here have previously been studied by Aquaro [l]1, Gulden [4], Kennison [5], Mansfield [6], Morita [7], and Poppe [9]. On the other hand, the concept of m-boundedness, introduced in §2, is new. Our main results (Theorems...
متن کاملLinearly Ordered Radon-nikodým Compact Spaces
We prove that every fragmentable linearly ordered compact space is almost totally disconnected. This combined with a result of Arvanitakis yields that every linearly ordered quasi Radon-Nikodým compact space is Radon-Nikodým, providing a new partial answer to the problem of continuous images of Radon-Nikodým compacta. It is an open problem posed by Namioka [8] whether the class of Radon-Nikodým...
متن کاملMetrizability of Topological Semigroups on Linearly Ordered Topological Spaces
The authors use techniques and results from the theory of generalized metric spaces to give a new, short proof that every connected, linearly ordered topological space that is a cancellative topological semigroup is metrizable, and hence embeddable in R. They also prove that every separable, linearly ordered topological space that is a cancellative topological semigroup is metrizable, so embedd...
متن کاملA Note on Point-countability in Linearly Ordered Spaces
In this note linearly ordered topological spaces (abbreviated LOTS) with a point-countable base are examined. It is shown that a LOTS is quasi-developable if and only if it has a <r-point-finite base and a LOTS with a point-countable base is paracompact. An example of a LOTS with a point-countable base that does not have a <r-point-finite base is given. Conditions are given for the metrizabilit...
متن کاملLinearly Ordered Topological Spaces and Weak Domain Representability
It is well known that domain representable spaces, that is topological spaces which are homeomorphic to the space of maximal elements of some domain, must be Baire. In this paper it is shown that every linearly ordered topological space (LOTS) is homeomorphic to an open dense subset of a weak domain representable space. This means that weak domain representable spaces need not be Baire. MR Clas...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1993
ISSN: 0166-8641
DOI: 10.1016/0166-8641(93)90057-k