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MACHINE SPACE I: WEAK EXPONENTIALS AND QUANTIFICATION OVER COMPACT SPACES
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AI
DOI：10.46298/LMCS-22(2:2)2026.png)
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Abstract
En 中文
. Topology may be interpreted as the study of verifiability, where opens correspond to semi-decidable properties. In this paper we make a distinction between verifiable properties themselves and processes which carry out the verification procedure. The former are simply opens, while we call the latter machines. Given a frame presentation OX = < G | R > we construct a space of machines Sigma Sigma Gwhose points are given by formal combinations of basic machines corresponding to generators in G. This comes equipped with an 'evaluation' map making it a weak exponential with base Sigma and exponent X. When it exists, the true exponential Sigma X occurs as a retract of machine space. We argue this helps explain why some spaces are exponentiable and others not. We then use machine space to study compactness by giving a purely topological version of Escard & oacute;'s algorithm for universal quantification over compact spaces in finite time. Finally, we relate our study of machine space to domain theory and domain embeddings.
Keywords:
Topology
Machine Space
Weak Exponential
Compactness
Domain Theory
Journal
L
IF:
1
Papers:
39
Citations:
0