On compact sets in the graph topology

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

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ON THREADING CONTINUOUS FUNCTIONS THROUGH COMPACT SETS

Real Analysis Exchange ◽

10.2307/44153417 ◽

1982 ◽

Vol 8 (2) ◽

pp. 455

Author(s):

Akemann ◽

Bruckner

Keyword(s):

Continuous Functions ◽

Compact Sets

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Relatively compact sets of Heisenberg manifolds

Differential Geometry and its Applications ◽

10.1016/j.difgeo.2021.101739 ◽

2021 ◽

Vol 76 ◽

pp. 101739

Author(s):

Sebastian Boldt

Keyword(s):

Compact Sets ◽

Heisenberg Manifolds

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A Weak Hadamard Smooth Renorming of L1(Ω, μ)

Canadian Mathematical Bulletin ◽

10.4153/cmb-1993-055-5 ◽

1993 ◽

Vol 36 (4) ◽

pp. 407-413 ◽

Cited By ~ 17

Author(s):

Jonathan M. Borwein ◽

Simon Fitzpatrick

Keyword(s):

Compact Sets ◽

Weakly Compact ◽

Weakly Compact Sets

AbstractWe show that L1(μ) has a weak Hadamard differential)le renorm (i.e. differentiable away from the origin uniformly on all weakly compact sets) if and only if μ is sigma finite. As a consequence several powerful recent differentiability theorems apply to subspaces of L1.

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