Johannes De Groot

Baayen, P.C.; Maurice, Maarten

doi:10.1016/0016-660x(73)90026-3

Cited by 3 publications

(2 citation statements)

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“…Linearizations in Hilbert spaces of actions of more general locally compact groups appear in [3] and [5], where earlier work of COPELAND and DE GROOT (E|4], [20]) was generalized. More information about the history of these results can be found in [3] and in [6].…”

Section: ~K> mentioning

confidence: 99%

Categories of topological transformation groups

Vries¹

1976

Lecture Notes in Mathematics

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Section: ~K> mentioning

confidence: 99%

Categories of topological transformation groups

Vries¹

1976

Lecture Notes in Mathematics

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“…Assuming the Hausdorff property, this is equivalent to the concept of a fc-space. de Groot [140]/ [17,18,45,327,339]. (3) This terminology is also in use [331,122,335,336] for spaces determined by countable subsets.…”

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confidence: 99%

Generalizations of the first axiom of countability

Siwiec¹

1975

Rocky Mountain J. Math.

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This paper is a comprehensive survey of the concepts which generalize first countability, of the relations among the concepts, and of the major examples found in the literature on the topic, 0. Introduction. There are several reasons which one may give to indicate the value of generalizing the first axiom of countability. Among these are the following:(1) To weaken assumptions in important theorems. For example, a closed image of a metric space is metrizable, if the range is assumed to be first countable.(2) To study important properties. For example, if a real valued function f is continuous upon restriction to each compact subspace of a space X, then / is continuous on X, if X is a /c-space.(3) To study sequences and their properties. For example, in first countable spaces every accumulation point of a subset A is the limit of a sequence in A.The emphasis in this article is on giving a comprehensive list of concepts which have been introduced to generalize first countability, from different points of view, along with examples and references. The reader may often judge the value of a concept by considering the number of references pertaining to it, as listed in our references in Section 1.The structure of this survey is as follows: In Section 1, we present a list of definitions of concepts which generalize first countability. For standard terminology we follow Kelley [199], Nagata [290], and Thron [379], and the reader may note that there are some remarks concerning notation and terminology at the beginning of Section 1. The reader is advised to skim Section 1 and refer to it as needed as he would a dictionary. The history of the subject is briefly surveyed in Section 2, along with some motivation for the concepts and some

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General Topology, in Particular Dimension Theory, in the Netherlands: The Decisive Influence of Brouwer’s Intuitionism

Koetsier

Mill

1997

Handbook of the History of General Topology

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Johannes De Groot

Cited by 3 publications

References 23 publications

Categories of topological transformation groups

Categories of topological transformation groups

Generalizations of the first axiom of countability

General Topology, in Particular Dimension Theory, in the Netherlands: The Decisive Influence of Brouwer’s Intuitionism

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