Journal of Formalized Mathematics
Volume 4, 1992
University of Bialystok
Copyright (c) 1992 Association of Mizar Users

## On Paracompactness of Metrizable Spaces

Leszek Borys
Warsaw University, Bialystok

### Summary.

The aim is to prove, using Mizar System, one of the most important result in general topology, namely the Stone Theorem on paracompactness of metrizable spaces [18]. Our proof is based on [17] (and also [15]). We prove first auxiliary fact that every open cover of any metrizable space has a locally finite open refinement. We show next the main theorem that every metrizable space is paracompact. The remaining material is devoted to concepts and certain properties needed for the formulation and the proof of that theorem (see also [4]).

#### MML Identifier: PCOMPS_2

The terminology and notation used in this paper have been introduced in the following articles [19] [7] [21] [1] [20] [10] [5] [6] [13] [12] [9] [14] [4] [16] [2] [22] [3] [11] [8]

#### Contents (PDF format)

1. Selected Properties of Real Numbers
2. Certain Functions Defined on Families of Sets
3. Paracompactness of Metrizable Spaces

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