On topological projective spaces and their Grassmannians
type: Item
instance of: scholarly article
title: On topological projective spaces and their Grassmannians
zbMATH Open document ID: 0715.51006
DOI: 10.1007/BF02942324
author: D. Kharzeev
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1989-01-01T00:00:00Z
review text: In an n-dimensional Desarguesian topological projective space \({\mathbb{P}}\) the sets \({\mathcal T}_ j\) of j-flats carry natural topologies \(\tau_ j\) for \(0\leq j<n\). The author shows that the topological spaces (\({\mathcal T}_ j,\tau_ j)\) are either all connected or all totally disconnected. Analogously, these spaces are either all compact or all non locally compact. It is known that the topologies \(\tau_ j\) are uniquely determined by \(\tau_ 0\). In the sequel of the paper the author assumes that only the sets \({\mathcal T}_ h\) and \({\mathcal T}_{h-1}\) are endowed with topologies for some \(0<h<n\). He investigates conditions which assure that these topologies turn \({\mathbb{P}}\) into a topological projective space with special emphasis on the case of locally compact and connected topologies.
reviewed by: Norbert Knarr
Mathematics Subject Classification ID: 51H10
Mathematics Subject Classification ID: 51M35
zbMATH DE Number: 4178011
zbMATH Keywords: Grassmannian
zbMATH Keywords: Desarguesian topological projective space
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02942324
OpenAlex ID: W1978064204
description: scientific article; zbMATH DE number 4178011