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The inductive limits and generalized metric properties of paratopological vector spaces

Kexiu Zhang

Abstract


In this paper, we mainly introduce the concept of the inductive limits of paratopological vector spaces, and obtain that every para-bornological space is the inductive limits of a family of quasi-normed spaces. Also, we discuss the local versus global properties on paratopological vector spaces, and show that a normally and locally paracompact (resp. locally metacompact, locally subparacompact) paratopological vector space is paracompact (resp. metacompact, subparacompact), which gives a partial answer to some questions of A.V. Arhangel’shii and M. Tkachenko. Moreover, we discuss the generalized metric properties on paratopological vector spaces. Some questions are posed concerning paratopological vector spaces.

Keywords


paratopological vector spaces; the inductive limits; local versus global properties; generalized metric properties.

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