Geodesic
The Zorn property for holomorphic functions
Thai Thuan Quang1 ; Duong Thanh Vy1 ; Le Thanh Hung2 ; Pham Hien Bang3
1 Department of Mathematics Quy Nhon University 170 An Duong Vuong Quy Nhon, Binh Dinh, Vietnam
2 Department of Mathematics Vinh Phuc College 2 Trung Trac Street Phuc Yen, Vinh Phuc, Vietnam
3 Department of Mathematics Thai Nguyen University of Education Luong Ngoc Quyen Street Thai Nguyen City, Vietnam
Annales Polonici Mathematici, Tome 120 (2017) no. 2, pp. 115-133

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The aim of this paper is to investigate Zorn’s property for the space $(E_B, \tau _E)$, where $E_B$ the linear hull of some compact, absolutely convex subset $B$ of a Fréchet space $E$ and the topology $\tau _E$ on $E_B$ is induced by the topology of $E.$ Furthermore, holomorphic extensions from $(E_B, \tau _E)$ are considered. Based on these results, we establish some results on extension of a Fréchet-valued continuous function $f$ to an entire function from a non-polar balanced convex compact subset $B$ of a Fréchet space whenever $f$ is approximated fast enough on $B$ by a sequence of polynomials.
DOI : 10.4064/ap170707-11-11
Keywords: paper investigate zorn property space tau where linear hull compact absolutely convex subset chet space topology tau induced topology furthermore holomorphic extensions tau considered based these results establish results extension chet valued continuous function entire function non polar balanced convex compact subset chet space whenever approximated fast enough sequence polynomials

Thai Thuan Quang 1 ; Duong Thanh Vy 1 ; Le Thanh Hung 2 ; Pham Hien Bang 3

1 Department of Mathematics Quy Nhon University 170 An Duong Vuong Quy Nhon, Binh Dinh, Vietnam
2 Department of Mathematics Vinh Phuc College 2 Trung Trac Street Phuc Yen, Vinh Phuc, Vietnam
3 Department of Mathematics Thai Nguyen University of Education Luong Ngoc Quyen Street Thai Nguyen City, Vietnam 
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Thai Thuan Quang; Duong Thanh Vy; Le Thanh Hung; Pham Hien Bang. The Zorn property for holomorphic functions. Annales Polonici Mathematici, Tome 120 (2017) no. 2, pp. 115-133. doi: 10.4064/ap170707-11-11

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