Locally connected compactifications

On Compactifications with Path Connected Remainders

We prove that every separable and metrizable space admits a metrizable compactification with a remainder that is both path connected and locally path connected. This result answers a question of P. Simon. Connectedness and compactness are two fundamental topological properties. A natural question is whether a given space admits a connected (Hausdorff) compactification. This question has been st...

Locally Connected Recursion Categories

A recursion category is locally connected if connected domains are jointly epimorphic. New proofs of the existence of non-complemented and recursively inseparable domains are given in a locally connected category. The use of local connectedness to produce categorical analogs of undecidable problems is new; the approach allows us to relax the hypotheses under which the results were originally pr...

Locally Connected Recurrent Networks

The fully connected recurrent network (FRN) using the on-line training method, Real Time Recurrent Learning (RTRL), is computationally expensive. It has a computational complexity of O(N 4) and storage complexity of O(N 3), where N is the number of non-input units. We have devised a locally connected recurrent model which has a much lower complexity in both computational time and storage space....

Embeddings of Locally Connected Compacta

Let A' be a ^-dimensional compactum and /: X -» M" a map into a piecewise linear n-manifold. n > k + 3. The main result of this paper asserts that if X is locally (2k ^-connected and / is (2k n + l)-connected, then / is homotopic to a CE equivalence. In particular, every ^--dimensional, /-connected, locally /--connected compactum is CE equivalent to a compact subset of R2*~r as long as r < k 3....

Locally-finite connected-homogeneous digraphs