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Closed and Open Maps for Partial Frames by John Frith; Anneliese Schauerte is a Mathematics article available to read on EtoBox.
What is Closed and Open Maps for Partial Frames about?
Abstract This paper concerns the notions of closed and open maps in the setting of partial frames, which, in contrast to full frames, do not necessarily have all joins. Examples of these include bounded distributive lattices, $$\sigma $$ σ - and $$\kappa $$ κ -frames and full frames. We define closed and open maps using geometrically intuitively appealing conditions involving preservation of closed, respectively open, congruences under certain maps. We then characterize them in terms of algebraic identities involving adjoints. We note that partial frame maps need have neither right nor left adjoints whereas frame maps of course always have right adjoints. The embedding of a partial frame in either its free frame or its congruence frame has proved illuminating and useful. We consider the conditions under which these embeddings are closed, open or skeletal. We then look at preservation and reflection of closed or open maps under the functors providing the free frame or the congruence frame. Points arise naturally in the construction of the spectrum functor for partial frames to partial spaces. They may be viewed as maps from the given partial frame to the 2-chain or as certain kinds
Who reads Closed and Open Maps for Partial Frames?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- John Frith; Anneliese Schauerte
- Publisher
- Springer Science and Business Media LLC
- Published
- 2023
- Language
- EN
- Field
- Mathematics (Physical Sciences)