On Exponential Mappings
DOI:
https://doi.org/10.58649/nkjpj703Keywords:
uniform space, uniformly continuous mapping, exponential mapping, exponential spaceAbstract
By a uniform space we shall mean a Hausdorff uniform space, and by a mapping – a uniformly continuous mapping between two uniform spaces. A uniformity U a space X induces a uniformity expc U of the exponential space expc X of non-empty compact subsets of X. In Section 2 we prove that if f : (X, U) → (Y, V ) is a precompact (uniformly perfect, pre-Lindelöf, twice uniformly continuous, uniformly quotient, uniformly paracompact, strongly uniformly paracompact, weakly uniformly paracompact, w(f) ≤ τ, (separable) metrizable) mapping, so is expc f : (expc X, expc U) → (expc Y, expc V ), where expc(f)(K) = fK.
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