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By extending adjacent-endpoint identification in Cantor’s space      N ( { 0 , 1 } ) N(\{ 0,1\} )       to Baire’s space      N ( A ) N(A)      , we move from the unit interval      I = L ( { 0 , 1 } ) I = L(\{ 0,1\} )       to      L ( A ) L(A)      . The metric spaces      L ( A ) n + 1 L{(A)^{n + 1}}       and      L ( A ) ∞  L{(A)^\infty }       have provided nonseparable analogues of Nöbeling’s and Urysohn’s imbedding theorems. To date, however,      L ( A ) L(A)       has no metric description. Here, we imbed      L ( A ) L(A)       in      l 2 ( A ) {l^2}(A)       and the induced metric yields a geometrical interpretation of      L ( A ) L(A)      . Except for the small last section, we are concerned with the imbedding. Once inside      l 2 ( A ) {l^2}(A)      , we see      L ( A ) L(A)       as a subspace of a "closed simplex"      Δ  A {\Delta ^A}       having the standard basis vectors together with the origin as vertices. The part of      L ( A ) L(A)       in each      n n      -dimensional face      σ  n {\sigma ^n}       of      Δ  A {\Delta ^A}       is a "generalized Sierpiński Triangle" called an      n n        -web       ω  n {\omega ^n}      . Topologically,      ω  n {\omega ^n}       is      L ( { 0 , 1 , …  , n } ) L(\{ 0,1, \ldots ,n\} )      . For      n = 2 , ω  2 n = 2,{\omega ^2}       is just the usual Sierpiński Triangle in      E 2 {E^2}      ; for      n = 3 , ω  3 n = 3,{\omega ^3}       is Mandelbrot’s fractal skewed web. Thus,      L ( A ) →  l 2 ( A ) L(A) \to {l^2}(A)       invites an extension of fractals. That is, when      | A | |A|       infinite, Baire’s Space      N ( A ) N(A)       is a "generalized code space" on      | A | |A|       symbols that addresses the points of the "generalized fractal"      L ( A ) L(A)      .

Lipscomb’s 𝐿(𝐴) space fractalized in Hilbert’s 𝑙²(𝐴) space