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]

#### Contents (PDF format)

1. Preliminaries
2. First-countable, Sequential, and {F}rechet Spaces
3. Counterexample of {F}rechet but Not First-countable Space
4. Auxiliary Theorems

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