Journal of Formalized Mathematics
Volume 10, 1998
University of Bialystok
Copyright (c) 1998
Association of Mizar Users
First-countable, Sequential, and Frechet Spaces
-
Bartlomiej Skorulski
-
University of Bialystok
Summary.
-
This article contains a definition of three classes of topological spaces:
first-countable, Frechet, and sequential. Next there are some facts about them, that
every first-countable space is Frechet and every Frechet space is sequential.
Next section contains a formalized construction of topological space which is
Frechet but not first-countable. This article is based
on [10, pp. 73-81].
MML Identifier:
FRECHET
The terminology and notation used in this paper have been
introduced in the following articles
[18]
[21]
[20]
[11]
[1]
[13]
[22]
[5]
[6]
[17]
[2]
[3]
[7]
[16]
[14]
[8]
[12]
[4]
[9]
[15]
[19]
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Preliminaries
-
First-countable, Sequential, and {F}rechet Spaces
-
Counterexample of {F}rechet but Not First-countable Space
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Auxiliary Theorems
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Received May 13, 1998
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