Title

Paralocalic groups

Document Type

Article

Publication Date

6-1-2019

Abstract

A paratoplogical group is a group equipped with a topology in which multiplication, but not necessarily inversion, is continuous. An example is the Sorgenfry line under addition. In the present paper, we propose a reasonable point-free version of this notion – a paralocailc group. We provide several examples and non-examples, and we list several unsolved problems. Among our examples, we show that addition does not induce the structure of a paralocailc group on the frame of opens of the Sorgenfrey line. This is related to the non-spatiality of the coproduct the Sorgenfry topology with itself.

Publication Source (Journal or Book title)

Topology and its Applications

First Page

275

Last Page

282

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