Axiomatic Foundation of Central Place Theory

The article refines the axiomatic foundation of central place theory (CPT) and identifies the possibilities and limitations of a logical transition in research from real settlement systems to central place (CP) systems. The necessity of relying on the CPT axioms in the following form is determined: (1) the space of a CP system is not infinite, but finite: the basis of each system is formed by an isolated lattice; the theory deals with physical space, not mathematical or geographical; (2) the space is homogeneous and isotropic in all respects, except for the distribution of not only the urban, but also the rural population; (3) a hexagonal lattice corresponds to the equilibrium state of an isolated CP system as an attractor; deviations from a hexagonal shape result only from external impact on the system; (4) CP systems are polymorphic: they can exist in modifications with both the same and different values for all levels of the hierarchy and not necessarily an integer value K ∈ (1, 7]. The axiom about a consumer’s “rational” behavior is accepted when establishing the CP hierarchy in terms of the volume of functions performed; when establishing their hierarchy in terms of population, it is redundant. In contrast to the foreign approach to CPT, which presupposes the transfer of properties of an ideal CP system to a real settlement system, in the approach of the Russian school, they are compared. The possibility of the latter is due to the equivalence principle in the relativistic version of the theory, according to which settlement systems form in the geographic space similarly to how CP systems form in the physical space. In both cases, if the gravitational effects are compensated, it is impossible to distinguish a settlement system from a CP system; i.e., a heterogeneous and anisotropic geographical space cannot be distinguished from a homogeneous and isotropic physical one. The immediate consequence of this is equivalence, on the one hand, of the population of settlements and CP, and, on the other, the distances between them in real settlement systems and CP systems

Axiom · Axiomatic system · Geometry · Hierarchy · Mathematical economics · Political science · Population · Pure mathematics · Sociology · Consumer Retail Behavior Studies · Law · Mathematics · Regional Economics and Spatial Analysis · Regional Socio-Economic Development Trends

• A Probability Model for Central Place Locations

  Michael F Dacey•Annals of the Association of…•1966

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