## Pták homomorphism theorem revisited.(English)Zbl 1050.46502

Summary: Rodrigues’ extension of the classical Pták’s homomorphism theorem to a non-necessarily locally convex setting states that a nearly semi-open mapping between a semi-B-complete space and an arbitrary topological vector space is semi-open [B. Rodrigues, J. Aust. Math. Soc., Ser. A 47, 322–333 (1989; Zbl 0708.46013)]. In this paper we study this extension and, as a consequence of the results obtained, provide an improvement of Pták’s homomorphism theorem.

### MSC:

 46A30 Open mapping and closed graph theorems; completeness (including $$B$$-, $$B_r$$-completeness)

### Keywords:

homomorphism theorem; B-complete space

Zbl 0708.46013
Full Text:

### References:

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