Document Type : Research Paper


1 Institute of Pure Mathematics, University of Tartu, J.Liivi street 2, EE-50409 Tartu, Estonia

2 Department of Mathematics, University of Latvia, Zellu street 8, LV-1002, Riga, Latvia and Institute of Mathematics and CS, University of Latvia, Raina bulv. 29, LV-1586, Riga, Latvia


The concept of an $L$-bornology is introduced and the theory of $L$-bornological spaces
is being developed. In particular the lattice of all $L$-bornologies on a given set is studied and basic properties of
the category of $L$-bornological spaces and bounded mappings are investigated.


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