Simple construction of spaces without the Hahn-Banach extension property

summary:An elementary construction for an abundance of vector topologies $\xi$ on a fixed infinite dimensional vector space $E$ such that $(E,\xi )$ has not the Hahn-Banach extension property but the topological dual $(E,\xi )'$ separates points of $E$ from zero is given

On the separable quotient problem for Banach spaces

While the classic separable quotient problem remains open, we survey general results related to this problem and examine the existence of a particular infinitedimensional separable quotient in some Banach spaces of vector-valued functions, linear operators and vector measures. Most of the results presented are consequence of known facts, some of them relative to the presence of complemented copies of the classic sequence spaces c_0 and l_p, for 1 <= p <= \infty. Also recent results of Argyros - Dodos - Kanellopoulos, and Sliwa are provided. This makes our presentation supplementary to a previous survey (1997) due to Mujica

Emptiness and becoming : integrating Madhyamika Buddhism and process philosophy

Beginning with a comparison of process philosophy and Madhyamika Buddhism -focussing in particular on Charles Hartshorne and Nagarjuna - which seeks to find points of similarity and difference, this thesis goes on to ask whether the differences are disagreements or complementary insights that may be integrated by means of a hermeneutical framework which can facilitate the enrichment of both systems. It is argued that process philosophy\u27s method of creative synthesis and Madhyamika\u27s method of negative dialectics are complementary rather than rival methods, because: (1) the Madhyamika bi-negation of symmetrical internal and external relations is complemented by process philosophy\u27s argument that asymmetrical relations have primacy, which can be integrated into a theory of \u27asymmetrical interdependence\u27; (2) the Madhyamika bi-negation of being and non-being is complemented by process philosophy\u27s argument that becoming has primacy; (3) Madhyamika\u27s emptiness (or openness) and process philosophy\u27s creativity are complementary ideas that can be integrated into a ‘creative emptiness’; (4) Madhyamika\u27s deconstruction of theism and acceptance of a conventional (and thus empty) ‘Cosmic Buddha-Bodhisattva’ and process philosophy\u27s panentheism are complementary and can be integrated in the idea of an ‘empty God’; (5) The creative emptiness and the empty God are two different but complementary ultimates - the ultimate activity and the ultimate actuality; (6) Madhyamika’s two truths -conventional (empty world) and ultimate (emptiness) - can be enriched by expanding the conventional to include ultimate actuality (empty God), and not subordinating the conventional to the ultimate; (7) process philosophy can be similarly enriched by meditating on creative emptiness, which reveals the empty God-world, which is not dominant vis-a-vis creative emptiness. An attempt is made to develop a hermeneutical framework for the comparison and integration of Madhyamika and process thought, which can also be used to construct a general theory of worldviews and a theory of interreligious dialogue. Finally, the practical applications of the integration of process thought and Madhyamika Buddhism are explored, focussing on ethical and socio-political issues and how the integration of the two systems can be used to advantage in these contexts